backup

src/bin/b.cc

@@ -24,13 +24,49 @@ using ull = uint64_t;
 #else
 using ll = long long;
 using ull = unsigned long long;
+using ld = long double;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
+using ld = long double;
 using pii = pair<int, int>;
 using pil = pair<int, ll>;
 using pli = pair<ll, int>;
 using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
 
 /* constants */
 constexpr int INF = 0x3f3f3f3f;
@@ -142,7 +178,9 @@ struct array_hash {
 #define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
 #define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
 #define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
 #define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
 template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
     set<T> st(__first, __last);
     size_t N = 0;
@@ -234,6 +272,7 @@ ll inverse(ll a, ll b) {
 }
 
 vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
     vector<tuple<int, int, ll>> res;
     for (int i = 2; i * i <= x; i++) {
         if (x % i == 0) {
@@ -249,6 +288,22 @@ vector<tuple<int, int, ll>> decompose(ll x) {
     return res;
 }
 
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
 /* string algorithms */
 vector<int> calc_next(string t) {  // pi function of t
   int n = (int)t.length();
@@ -327,6 +382,14 @@ template <ll mdl>
 istream& operator>>(istream& in, MLL<mdl>& num) {
     return in >> num.val;
 }
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
 /////////////////////////////////////////////////////////
 
 #define SINGLE_TEST_CASE
@@ -340,25 +403,19 @@ void prep() {}
 
 void solve() {
     read(int, n, k);
-    vector<int> pos(n + 1);
-    vector<int> a;
-    for (int i = 0; i < n; ++i) {
-        read(int, x);
-        a.emplace_back(x);
-        pos[x] = i;
+    readvec(int, a, n);
+    int ptr = 0;
+    int empty = k;
+    int cnt = 0;
+    while (ptr < n) {
+        if (empty < a[ptr]) {
+            cnt += 1;
+            empty = k;
+        } else {
+            empty -= a[ptr++];
         }
-    vector<int> res(n);
-    if (k > n or k == 1) {
-        cout << -1 << '\n';
-        return;
     }
-    for (int i = 1; i <= k; ++i) {
-        res[pos[i % k + 1]] = i;
-    }
-    for (int i = k + 1; i <= n; ++i) {
-        res[pos[i]] = i;
-    }
-    putvec(res);
+    cout << cnt + 1 << '\n';
 }
 
 int main() {

src/bin/c.cc

@@ -24,13 +24,49 @@ using ull = uint64_t;
 #else
 using ll = long long;
 using ull = unsigned long long;
+using ld = long double;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
+using ld = long double;
 using pii = pair<int, int>;
 using pil = pair<int, ll>;
 using pli = pair<ll, int>;
 using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
 
 /* constants */
 constexpr int INF = 0x3f3f3f3f;
@@ -142,7 +178,9 @@ struct array_hash {
 #define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
 #define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
 #define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
 #define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
 template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
     set<T> st(__first, __last);
     size_t N = 0;
@@ -234,6 +272,7 @@ ll inverse(ll a, ll b) {
 }
 
 vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
     vector<tuple<int, int, ll>> res;
     for (int i = 2; i * i <= x; i++) {
         if (x % i == 0) {
@@ -249,6 +288,22 @@ vector<tuple<int, int, ll>> decompose(ll x) {
     return res;
 }
 
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
 /* string algorithms */
 vector<int> calc_next(string t) {  // pi function of t
   int n = (int)t.length();
@@ -327,6 +382,14 @@ template <ll mdl>
 istream& operator>>(istream& in, MLL<mdl>& num) {
     return in >> num.val;
 }
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
 /////////////////////////////////////////////////////////
 
 #define SINGLE_TEST_CASE
@@ -338,25 +401,45 @@ void dump_ignore() {}
 
 void prep() {}
 
+template<typename T>
+struct BIT {
+    int n;
+    vector<T> c;
+    BIT(size_t n) : n(n), c(n + 1) {}
+    void add(size_t i, const T& k) {
+        while (i <= n) {
+            c[i] += k;
+            i += lowbit(i);
+        }
+    }
+    T getsum(size_t i) {
+        T res = {};
+        while (i) {
+            res += c[i];
+            i -= lowbit(i);
+        }
+        return res;
+    }
+};
+
 void solve() {
-    read(string, s);
-    int n = s.size();
-    if (n == 1) {
-        if ((s[0] - 48) % 4 == 0) {
-            cout << 0 << '\n';
-        } else {
-            cout << -1 << '\n';
+    read(int, n);
+    readvec(ll, a, n);
+    auto [N, mp] = discretize<ll>(a.begin(), a.end());
+    BIT<int> tr(N);
+    ll res = 0;
+    ll sum = 0;
+    for (int i = n - 1; ~i; --i) {
+        res += a[i] * (n - 1 - i) + sum;
+        auto it = mp.lower_bound(100'000'000 - a[i]);
+        if (it != mp.end()) {
+            ll cnt = tr.getsum(N) - tr.getsum(max((unsigned long)0, it->second - 1));
+            res -= cnt * 100'000'000;
         }
+        tr.add(mp[a[i]], 1);
+        sum += a[i];
     }
-    for (int i = 0; i < n; ++i) {
-        int a = s[mod(n - 1 + i, n)], b = s[mod(n - 2 + i, n)];
-        int num = (b - '0') * 10 + (a - '0');
-        if (num % 4 == 0) {
-            cout << i << '\n';
-            return;
-        }
-    }
-    cout << -1 << '\n';
+    cout << res << '\n';
 }
 
 int main() {

src/bin/cf-1842e.cc

@@ -0,0 +1,602 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+struct point {
+    int x, y, c;
+    point(int x, int y, int c) : x(x), y(y), c(c) {}
+};
+
+template<typename Addable_Info_t, typename Tag_t, typename Sequence = std::vector<Addable_Info_t>> class segtree {
+private:
+    using size_type = uint64_t;
+    using info_type = Addable_Info_t;
+    using tag_type = Tag_t;
+    size_type _max;
+    vector<info_type> d;
+    vector<tag_type> b;
+    void pull(size_type p) {
+        d[p] = d[p * 2] + d[p * 2 + 1];
+    }
+    void push(size_type p, size_type left_len, size_type right_len) {
+        d[p * 2].apply(b[p], left_len), d[p * 2 + 1].apply(b[p], right_len);
+        b[p * 2].apply(b[p]), b[p * 2 + 1].apply(b[p]);
+        b[p] = tag_type();
+    }
+    void set(size_type s, size_type t, size_type p, size_type x, const info_type& c) {
+        if (s == t) {
+            d[p] = c;
+            return;
+        }
+        size_type m = s + (t - s >> 1);
+        if (s != t) push(p, m - s + 1, t - m);
+        if (x <= m) set(s, m, p * 2, x, c);
+        else set(m + 1, t, p * 2 + 1, x, c);
+        d[p] = d[p * 2] + d[p * 2 + 1];
+    }
+    
+    void range_apply(size_type s, size_type t, size_type p, size_type l, size_type r, const tag_type& c) {
+        if (l <= s && t <= r) {
+            d[p].apply(c, t - s + 1);
+            b[p].apply(c);
+            return;
+        }
+        size_type m = s + (t - s >> 1);
+        push(p, m - s + 1, t - m);
+        if (l <= m) range_apply(s, m, p * 2, l, r, c);
+        if (r > m)  range_apply(m + 1, t, p * 2 + 1, l, r, c);
+        pull(p);
+    }
+    info_type range_query(size_type s, size_type t, size_type p, size_type l, size_type r) {
+        if (l <= s && t <= r) {
+            return d[p];
+        }
+        size_type m = s + (t - s >> 1);
+        info_type res = {};
+        push(p, m - s + 1, t - m);
+        if (l <= m) res = res + range_query(s, m, p * 2, l, r);
+        if (r > m)  res = res + range_query(m + 1, t, p * 2 + 1, l, r);
+        return res;
+    }
+    void build(const Sequence& a, size_type s, size_type t, size_type p) {
+        if (s == t) {
+            d[p] = a[s];
+            return;
+        }
+        int m = s + (t - s >> 1);
+        build(a, s, m, p * 2);
+        build(a, m + 1, t, p * 2 + 1);
+        pull(p);
+    }
+public:
+    segtree(size_type __max) : d(4 * __max), b(4 * __max), _max(__max - 1) {}
+    segtree(const Sequence& a) : segtree(a.size()) {
+        build(a, {}, _max, 1);
+    }
+    void set(size_type i, const info_type& c) {
+        set({}, _max, 1, i, c);
+    }
+    
+    void range_apply(size_type l, size_type r, const tag_type& c) {
+        range_apply({}, _max, 1, l, r, c);
+    }
+    void apply(size_type i, const tag_type& c) {
+        range_apply(i, i, c);
+    }
+    info_type range_query(size_type l, size_type r) {
+        return range_query({}, _max, 1, l, r);
+    }
+    info_type query(size_type i) {
+        return range_query(i, i);
+    }
+    Sequence serialize() {
+        Sequence res = {};
+        for (size_type i = 0; i <= _max; ++i) {
+            res.push_back(query(i));
+        }
+        return res;
+    }
+    const vector<info_type>& get_d() {
+        return d;
+    }
+};
+struct Tag {
+    ll val = 0;
+    void apply(const Tag& rhs) {
+        val += rhs.val;
+    }
+};
+struct Info {
+    ll val = INFLL;
+    void apply(const Tag& rhs, size_t len) {
+        val += rhs.val;
+    }
+};
+Info operator+(const Info &a, const Info &b) {
+    return {min(a.val, b.val)};
+}
+
+void solve() {
+    read(int, n, k, A);
+    vector<point> pts;
+    vector<vector<point>> open(k + 1);
+    for (int i = 0; i < n; ++i) {
+        read(int, x, y, c);
+        pts.emplace_back(x, y, c);
+        open[x].emplace_back(x, y, c);
+    }
+    segtree<Info, Tag> tr(k + 1);
+    for (int i = 0; i <= k; ++i) {
+        tr.set(i, {0});
+    }
+    auto cmp = [] (const point& a, const point& b) { return a.y < b.y; };
+    priority_queue<point, vector<point>, decltype(cmp)> stack(cmp);
+    ll sum = 0;
+    ll res = INFLL;
+    ll prev_dp = 0;
+    for (int i = 0; i <= k; ++i) {
+        int x = i, y = k - x;
+        // debug(x);
+        ll dp = INFLL;
+        while (stack.size() and stack.top().y > y) {
+            auto [x, y, c] = stack.top();
+            stack.pop();
+            tr.range_apply(x, k, {c});
+            // cerr << "sum -= " << c << endl;
+            sum -= c;
+        }
+        ll me = 0;
+        for (auto&& [x, y, c] : open[x]) {
+            tr.range_apply(x, k, {-c});
+            stack.emplace(x, y, c);
+            sum += c;
+            // cerr << "sum += " << c << endl;
+            me += c;
+        }
+        dp = min(dp, me + prev_dp);
+        while (stack.size() and stack.top().y == y) {
+            auto [x, y, c] = stack.top();
+            stack.pop();
+            tr.range_apply(x, k, {c});
+            sum -= c;
+            // cerr << "sum -= " << c << endl;
+        }
+        if (x) {
+            // for (auto&& x : tr.serialize()) cerr << x.val << ' ';
+            // cerr << endl;
+            // debug(sum);
+            dp = min(dp, A * (x - 1) + tr.range_query(0, x - 1).val + sum);
+            dp = min(dp, A * x + sum);
+        }
+        // debug(dp);
+        tr.apply(x, {dp - A * x});
+        res = dp;
+        prev_dp = dp;
+    }
+    cout << res << '\n';
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1845d.cc

@@ -0,0 +1,472 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+template<typename _Tp, typename _Op = function<_Tp(const _Tp&, const _Tp&)>> struct sparse_table {
+    _Op op;
+    vector<vector<_Tp>> st;
+    template <typename ReverseIterator>
+    sparse_table(ReverseIterator __first, ReverseIterator __last, _Op&& __operation) {
+        op = __operation;
+        int n = distance(__first, __last);
+        st = vector<vector<_Tp>>(n, vector<_Tp>(int(log2(n) + 1)));
+        int i = n - 1;
+        for (auto it = __first; it != __last; ++it) {
+            st[i][0] = *it;
+            for (int j = 1; i + (1 << j) <= n; ++j) {
+                st[i][j] = op(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
+            }
+            i -= 1;
+        }
+    }
+    _Tp query(size_t __start, size_t __end) {
+        int s = lg2(__end - __start + 1);
+        return op(st[__start][s], st[__end - (1 << s) + 1][s]);
+    }
+};
+
+auto u_min = [] (ll a, ll b) { return min(a, b); };
+
+void solve() {
+    read(int, n);
+    readvec(int, a, n);
+    vector<ll> ps(n + 1);
+    for (int i = 1; i <= n; ++i) {
+        ps[i] = ps[i - 1] + a[i - 1];
+    }
+    sparse_table<ll> st(ps.rbegin(), ps.rend(), u_min);
+    ll delta = 0, var_delta = ps[n];
+    for (int i = 0; i < n; ++i) {
+        ll curr = st.query(i + 1, n) - ps[i];
+        if (curr < -delta) {
+            delta = -curr;
+            var_delta = ps[i];
+        }
+    }
+    cout << var_delta << '\n';
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1851g.cc

@@ -0,0 +1,503 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+struct query {
+    int idx, u, v;
+    ll e;
+};
+
+class quick_union {
+private:
+    vector<size_t> c, sz;
+public:
+    quick_union(size_t n) : c(n), sz(n) {
+        iota(c.begin(), c.end(), 0);
+        sz.assign(n, 1);
+    }
+    
+    size_t query(size_t i) {
+        if (c[i] != i) c[i] = query(c[i]);
+        return c[i];
+    }
+    
+    void merge(size_t i, size_t j) {
+        if (connected(i, j)) return;
+        sz[query(j)] += sz[query(i)];
+        c[query(i)] = query(j);
+    }
+    bool connected(size_t i, size_t j) {
+        return query(i) == query(j);
+    }
+    size_t query_size(size_t i) {
+        return sz[query(i)];
+    }
+};
+
+void solve() {
+    read(int, n, m);
+    vector<ll> h(n + 1);
+    for (int i = 1; i <= n; ++i) cin >> h[i];
+    vector<pii> edges;
+    for (int i = 0; i < m; ++i) {
+        read(int, u, v);
+        edges.emplace_back(u, v);
+    }
+    sort_by_key(edges.begin(), edges.end(), [&] (const pii& a) { return max(h[a.first], h[a.second]); });
+    read(int, q);
+    vector<query> qs;
+    for (int i = 0; i < q; ++i) {
+        read(int, u, v, e);
+        qs.push_back({i, u, v, e});
+    }
+    sort_by_key(qs.begin(), qs.end(), [&] (const query& a) { return h[a.u] + a.e; });
+    ll curr_mn = 0;
+    int ptr = 0;
+    quick_union qu(n + 1);
+    vector<bool> res(q);
+    for (auto&& [u, v] : edges) {
+        curr_mn = max(curr_mn, max(h[u], h[v]));
+        while (ptr < q and h[qs[ptr].u] + qs[ptr].e < curr_mn) {
+            res[qs[ptr].idx] = qu.connected(qs[ptr].u, qs[ptr].v);
+            ++ptr;
+        }
+        qu.merge(u, v);
+    }
+    while (ptr < q) {
+        res[qs[ptr].idx] = qu.connected(qs[ptr].u, qs[ptr].v);
+        ++ptr;
+    }
+    for (int i = 0; i < q; ++i) {
+        if (res[i]) {
+            cout << "YES\n";
+        } else {
+            cout << "NO\n";
+        }
+    }
+    cout << endl;
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1856d.cc

@@ -0,0 +1,455 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+void solve() {
+    read(int, n);
+    // 0 for less, 1 for greater
+    auto compare = [&] (int i, int j) -> bool {
+        cout << "? " << i << ' ' << j << endl;
+        read(ll, x);
+        ll y;
+        if (i + 1 == j) {
+            y = 0;
+        } else {
+            cout << "? " << i + 1 << ' ' << j << endl;
+            cin >> y;
+        }
+        if (x == y + j - i) {
+            return 1;
+        } else {
+            return 0;
+        }
+    };
+    auto dfs = [&] (auto dfs, int l, int r) -> int {
+        if (l == r) {
+            return l;
+        }
+        int mid = l + r >> 1;
+        int left = dfs(dfs, l, mid), right = dfs(dfs, mid + 1, r);
+        if (compare(left, right)) {
+            return left;
+        } else {
+            return right;
+        }
+    };
+    int res = dfs(dfs, 1, n);
+    cout << "! " << res << endl;
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1857d.cc

@@ -0,0 +1,497 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define adjw(ch, n) __AS_PROCEDURE(vector<vector<pil>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+class quick_union {
+private:
+    vector<size_t> c, sz;
+public:
+    quick_union(size_t n) : c(n), sz(n) {
+        iota(c.begin(), c.end(), 0);
+        sz.assign(n, 1);
+    }
+    
+    size_t query(size_t i) {
+        if (c[i] != i) c[i] = query(c[i]);
+        return c[i];
+    }
+    
+    void merge(size_t i, size_t j) {
+        if (connected(i, j)) return;
+        sz[query(j)] += sz[query(i)];
+        c[query(i)] = query(j);
+    }
+    bool connected(size_t i, size_t j) {
+        return query(i) == query(j);
+    }
+    size_t query_size(size_t i) {
+        return sz[query(i)];
+    }
+};
+
+using mll = MLL<PRIME>;
+mll pow(mll a, ll b) {
+    mll res;
+    if (b == 0) {
+        res = 1;
+    } else if (b == 1) {
+        res = a;
+    } else {
+        res = pow(a, b / 2);
+        res = res * res;
+        if (b / 2 * 2 != b) {
+            res *= a;
+        }
+    }
+    return res;
+}
+
+void solve() {
+    using mll = MLL<PRIME>;
+    read(int, n, s);
+    vector<tiii> edges;
+    for (int i = 0; i < n - 1; ++i) {
+        read(int, u, v, w);
+        edges.emplace_back(w, u, v);
+    }
+    sort(edges.begin(), edges.end());
+    quick_union qu(n + 1);
+    vector<ll> cnt;
+    ll pre = 0;
+    for (auto&& [w, u, v] : edges) {
+        ll prev_u = qu.query_size(u), prev_v = qu.query_size(v);
+        qu.merge(u, v);
+        ll curr = prev_u * prev_v - 1;
+        cnt.emplace_back(curr);
+        pre = curr;
+    }
+    int prev = s;
+    mll opt = 1;
+    mll res = 1;
+    for (int i = n - 2; ~i; --i) {
+        ll curr = cnt[i];
+        int w = get<0>(edges[i]);
+        opt += max(0, prev - w);
+        if (curr) res *= pow(opt, curr);
+        prev = w;
+    }
+    cout << res << '\n';
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1896d.cc

@@ -0,0 +1,463 @@
+#include <numeric>
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+void solve() {
+    read(int, n, q);
+    readvec(int, a, n);
+    int cnt1 = count(a.begin(), a.end(), 1);
+    int tot = accumulate(a.begin(), a.end(), 0);
+    while (q--) {
+        read(int, op);
+        if (op == 1) {
+            read(int, s);
+            if (cnt1) {
+                if (s >= 0 and s <= tot) {
+                    cout << "YES\n";
+                } else {
+                    cout << "NO\n";
+                }
+            } else {
+                if (s >= 0 and s <= tot and (s & 1) == 0) {
+                    cout << "YES\n";
+                } else {
+                    cout << "NO\n";
+                }
+            }
+        } else {
+            read(int, i, v);
+            --i;
+            tot -= a[i];
+            cnt1 -= a[i] == 1;
+            a[i] = v;
+            tot += v;
+            cnt1 += a[i] == v;
+        }
+    }
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1907f.cc

@@ -0,0 +1,485 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+void solve() {
+    read(int, n);
+    readvec(int, a, n);
+    // increasing
+    int res = INF;
+    {
+        int f = 1;
+        int tp = -1;;
+        for (int i = 1; i < n; ++i) {
+            if (a[i] < a[i - 1]) {
+                if (tp != -1) {
+                    f = 0;
+                    break;
+                } else {
+                    tp = i;
+                    // (i - 1, i)
+                }
+            }
+        }
+        if (f) {
+            if (tp == -1) {
+                res = 0;
+            } else {
+                if (a[n - 1] <= a[0]) {
+                    res = min(res, min(n - tp, 2 + tp));
+                }
+            }
+        }
+    }
+    // increasing
+    {
+        int f = 1;
+        int tp = -1;;
+        for (int i = 1; i < n; ++i) {
+            if (a[i] > a[i - 1]) {
+                if (tp != -1) {
+                    f = 0;
+                    break;
+                } else {
+                    tp = i;
+                    // (i - 1, i)
+                }
+            }
+        }
+        if (f) {
+            if (tp == -1) {
+                res = min(res, 1);
+            } else {
+                if (a[n - 1] >= a[0]) {
+                    res = min(res, min(1 + n - tp, 1 + tp));
+                }
+            }
+        }
+    }
+    cout << (res == INF ? -1 : res) << '\n';
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1931f.cc

@@ -0,0 +1,489 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+void solve() {
+    read(int, n, k);
+    vector<vector<int>> a(k);
+    for (int i = 0; i < k; ++i) {
+        readvec(int, x, n);
+        a[i] = x;
+    }
+    if (k == 1) {
+        cout << "YES\n";
+    } else if (k == 2) {
+        int x = a[0][0], y = a[1][0];
+        int f = 1;
+        int l = 0, r = 0;
+        while (l < n and r < n) {
+        }
+    } else {
+        int x = a[0][0], y = a[1][0];
+        int pre_x = -1, pre_y = -1;
+        for (int i = 1; i < n; ++i) {
+            if (a[0][i] == y) {
+                pre_y = i;
+            }
+        }
+        for (int i = 1; i < n; ++i) {
+            if (a[1][i] == x) {
+                pre_x = i;
+            }
+        }
+        vector<int> p;
+        int insert_pos = -1;
+        for (int i = 1; i < n; ++i) {
+            if (a[0][i] != x) {
+                p.emplace_back(a[0][i]);
+            }
+            if (a[0][i] == pre_x) {
+                insert_pos = i;
+                p.emplace_back(-1), p.emplace_back(-1);
+            }
+        }
+        if (pre_x == pre_y) {
+            // x y
+            int f = 0;
+            for (int i = 2; i < k; ++i) {
+                for (int j = 1; j < n; ++j) {
+                    if (minmax(a[i][j - 1], a[i][j]) == minmax(x, y)) {
+                        p[insert_pos] = a[i][j - 1];
+                        p[insert_pos + 1] = a[i][j];
+                        f = 1;
+                        break;
+                    }
+                }
+            }
+            if ((not f) and k != 2) {
+                cout << "NO\n";
+            } else {
+                
+            }
+        }
+    }
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1971b.cc

@@ -0,0 +1,442 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+void solve() {
+    read(string, s);
+    int n = s.size();
+    for (int i = 1; i < n; ++i) {
+        if (s[i] != s[i - 1]) {
+            swap(s[i], s[i - 1]);
+            cout  << "YES\n";
+            cout << s << '\n';
+            return;
+        }
+    }
+    cout << "NO\n";
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1971c.cc

@@ -0,0 +1,438 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+void solve() {
+    read(int, a, b, c, d);
+    if (a > b) swap(a, b);
+    if (c > a and c < b and d > a and d < b or (c < a or c > b) and (d < a or d > b)) {
+        cout << "NO\n";
+    } else {
+        cout << "YES\n";
+    }
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1971d.cc

@@ -0,0 +1,445 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+void solve() {
+    read(string, s);
+    int n = s.size();
+    int cnt = 0;
+    int has_01 = 0;
+    for (int i = 1; i < n; ++i) {
+        if (s[i] != s[i - 1]) {
+            if (s[i - 1] == '0') {
+                has_01 = 1;
+            }
+            cnt += 1;
+        }
+    }
+    if (has_01) cnt = max(0, cnt - 1);
+    cout << cnt + 1 << '\n';
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1971e.cc

@@ -0,0 +1,455 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+void solve() {
+    read(ll, n, k, q);
+    vector<ll> a(k + 1), b(k + 1);
+    for (int i = 1; i <= k; ++i) cin >> a[i];
+    for (int i = 1; i <= k; ++i) cin >> b[i];
+    while (q--) {
+        read(ll, d);
+        int l = 0, r = k;
+        while (l < r) {
+            int mid = l + r + 1 >> 1;
+            if (a[mid] <= d) {
+                l = mid;
+            } else {
+                r = mid - 1;
+            }
+        }
+        
+        if (a[l] == d) {
+            cout << b[l] << ' ';
+        } else {
+            double res = double(1) * (d - a[l]) / (a[l + 1] - a[l]) * (b[l + 1] - b[l]);
+            cout << int(b[l] + res) << ' ';
+        }
+    }
+    cout << endl;
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1971f.cc

@@ -0,0 +1,443 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+ll calc(ll r) {
+    ll res = 0;
+    for (ll x = -r; x <= r; ++x) {
+        ll rg = (ll(ceil(sqrt((long double)(r * r) - x * x))) - 1);
+        if (rg < 0) continue;
+        else res += 2 * rg + 1;
+    }
+    return res;
+}
+
+void solve() {
+    read(ll, r);
+    cout << calc(r + 1) - calc(r) << '\n';
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1971h.cc

@@ -0,0 +1,561 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+namespace tarjan {
+    struct mutex_cond {
+        int v1; bool cond1;
+        int v2; bool cond2;
+        mutex_cond(int v1, bool cond1, int v2, bool cond2) : v1(v1), cond1(cond1), v2(v2), cond2(cond2) {}
+    };
+    struct inclusive_cond {
+        int v1; bool cond1;
+        int v2; bool cond2;
+        inclusive_cond(int v1, bool cond1, int v2, bool cond2) : v1(v1), cond1(cond1), v2(v2), cond2(cond2) {}
+    };
+    // Returns the mapping between vertices and their affiliated sccs.
+    vector<int> scc(const vector<vector<int>>& ch) {
+        int n = ch.size();
+        int cnt = 0, scn = 0;
+        vector<int> dfn(n), low(n), vis(n), st;
+        vector<int> br(n);
+        auto tarjan = [&] (auto tarjan, int v) -> void {
+            dfn[v]=low[v]=++cnt;
+            st.push_back(v);
+            vis[v]=1;
+            for(const auto&u:ch[v])
+                if(!dfn[u]) tarjan(tarjan, u),low[v]=min(low[v],low[u]);
+                else if(vis[u])low[v]=min(low[v],dfn[u]);
+            if(dfn[v]==low[v]){
+                ++scn;
+                int u;
+                do u=st.back(), st.pop_back(),vis[u]=0,br[u]=scn; while(u!=v);
+            }
+        };
+        for (int i = 0; i < n; ++i) {
+            if (!dfn[i]) {
+                tarjan(tarjan, i);
+            }
+        }
+        return br;
+    }
+    // This method can eliminate redundant edges or self-loops
+    vector<vector<int>> build_scc(const vector<vector<int>>& ch) {
+        int n = ch.size();
+        auto br = scc(ch);
+        int cnt = *max_element(br.begin(), br.end());
+        vector<unordered_set<int, safe_hash>> rb(cnt + 1);
+        for (int i = 0; i < n; ++i) {
+            for (auto&& u : ch[i]) {
+                if (br[i] != br[u]) rb[br[i]].emplace(br[u]);
+            }
+        }
+        vector<vector<int>> res(cnt + 1);
+        for (int i = 1; i <= cnt; ++i) {
+            res[i] = vector<int>(rb[i].begin(), rb[i].end());
+        }
+        return res;
+    }
+    
+    // This method can eliminate redundant edges or self-loops
+    // return form: (scc size, children of scc)
+    vector<pair<size_t, vector<int>>> build_scc_with_size(const vector<vector<int>>& ch) {
+        int n = ch.size();
+        auto br = scc(ch);
+        int cnt = *max_element(br.begin(), br.end());
+        vector<unordered_set<int, safe_hash>> rb(cnt + 1);
+        for (int i = 0; i < n; ++i) {
+            for (auto&& u : ch[i]) {
+                if (br[i] != br[u]) rb[br[i]].emplace(br[u]);
+            }
+        }
+        vector<pair<size_t, vector<int>>> res(cnt + 1);
+        for (int i = 1; i <= cnt; ++i) {
+            res[i].second = vector<int>(rb[i].begin(), rb[i].end());
+        }
+        for (int i = 1; i <= n; ++i) {
+            res[br[i]].first += 1;
+        }
+        return res;
+    }
+    // indices start from 1, result has `n` items
+    optional<vector<bool>> solve_twosat(int n, const vector<mutex_cond>& conditions) {
+        vector<vector<int>> ch(2 * n + 1);
+        for (auto&& [v1, cond1, v2, cond2] : conditions) {
+            ch[(1 ^ cond1) * n + v1].emplace_back(cond2 * n + v2);
+            ch[(1 ^ cond2) * n + v2].emplace_back(cond1 * n + v1);
+        }
+        auto sccno = scc(ch);
+        for (int i = 1; i <= n; ++i) {
+            if (sccno[i] == sccno[i + n]) {
+                return nullopt;
+            }
+        }
+        vector<bool> res;
+        for (int i = 1; i <= n; ++i) {
+            if (sccno[i] < sccno[i + n]) {
+                res.emplace_back(false);
+            } else {
+                res.emplace_back(true);
+            }
+        }
+        return res;
+    };
+    // indices start from 1, result has `n` items
+    optional<vector<bool>> solve_twosat(int n, const vector<inclusive_cond>& conditions) {
+        vector<mutex_cond> trans_conds;
+        for (auto&& [v1, cond1, v2, cond2] : conditions) {
+            trans_conds.emplace_back(v1, cond1, v2, not cond2);
+        }
+        return solve_twosat(n, trans_conds);
+    }
+}
+
+void solve() {
+    read(int, n);
+    vector<vector<int>> a(3, vector<int>(n));
+    for (int i = 0; i < 3; ++i) {
+        for (int j = 0; j < n; ++j) {
+            cin >> a[i][j];
+        }
+    }
+    vector<tarjan::mutex_cond> conditions;
+    auto sgn = [] (int x) { return (abs(x) / x + 1) / 2; };
+    for (int i = 0; i < n; ++i) {
+        for (int j = 0; j < 2; ++j) {
+            for (int k = j + 1; k < 3; ++k) {
+                conditions.emplace_back(abs(a[j][i]), sgn(a[j][i]), abs(a[k][i]), sgn(a[k][i]));
+            }
+        }
+    }
+    if (tarjan::solve_twosat(n, conditions).has_value()) {
+        cout << "YES\n";
+    } else {
+        cout << "NO\n";
+    }
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/ctext_out.cc

@@ -28,10 +28,43 @@ using ld = long double;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
+using ld = long double;
 using pii = pair<int, int>;
 using pil = pair<int, ll>;
 using pli = pair<ll, int>;
 using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
 template <typename T> using max_heap = priority_queue<T>;
 template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
 
@@ -145,7 +178,9 @@ struct array_hash {
 #define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
 #define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
 #define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
 #define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
 template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
     set<T> st(__first, __last);
     size_t N = 0;
@@ -237,6 +272,7 @@ ll inverse(ll a, ll b) {
 }
 
 vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
     vector<tuple<int, int, ll>> res;
     for (int i = 2; i * i <= x; i++) {
         if (x % i == 0) {
@@ -252,6 +288,22 @@ vector<tuple<int, int, ll>> decompose(ll x) {
     return res;
 }
 
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
 /* string algorithms */
 vector<int> calc_next(string t) {  // pi function of t
   int n = (int)t.length();
@@ -330,73 +382,149 @@ template <ll mdl>
 istream& operator>>(istream& in, MLL<mdl>& num) {
     return in >> num.val;
 }
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
 /////////////////////////////////////////////////////////
 
-#define SINGLE_TEST_CASE
-// #define DUMP_TEST_CASE 7219
-
-void dump() {}
-
-void dump_ignore() {}
-
-void prep() {}
-
-void solve() {
-    read(int, n, m);
-    vector<vector<pil>> e(n + 1);
-    while (m--) {
-        read(int, u, v);
-        read(ll, w);
-        e[u].emplace_back(v, w * 2);
-        e[v].emplace_back(u, w * 2);
+class Solution {
+public:
+    vector<int> findProductsOfElements(vector<vector<long long>>& queries) {
+        vector<int> rres;
+        for (auto&& v : queries) {
+            ll left = v[0] + 1, right = v[1] + 1, mdl = v[2];
+            vector<ll> dp(64);
+            vector<ll> cnt(64);
+            dp[1] = 1;
+            cnt[1] = 1;
+            for (int i = 2; i < 64; ++i) {
+                if (cnt[i - 1] > LLONG_MAX / 3) {
+                    cnt[i] = LLONG_MAX;
+                } else {
+                    cnt[i] = cnt[i - 1] * 3 + 1;
                 }
-    for (int i = 1; i <= n; ++i) {
-        read(ll, x);
-        e[0].emplace_back(i, x);
-        e[i].emplace_back(0, x);
             }
-    min_heap<pli> pq;
-    pq.emplace(0, 0);
-    vector<bool> vis(n + 1);
-    vector<ll> dis(n + 1, INFLL);
-    while (pq.size()) {
-        poptop(pq, d, v);
-        continue_or(vis[v], 1);
-        dis[v] = d;
-        for (auto&& [u, w] : e[v]) {
-            if (d + w < dis[u]) {
-                dis[u] = d + w;
-                pq.emplace(dis[u], u);
+            unordered_map<ll, ll, safe_hash> cache;
+            cache[0] = 1;
+            auto pow = [&] (auto pow, ll b, ll m) -> ll {
+                if (cache[m]) return cache[m];
+                ll curr = pow(pow, b, m / 2);
+                cache[m] = ((((curr * curr) % mdl) * ((m & 1) ? (b % mdl) : 1)) % mdl);
+                return cache[m];
+            };
+            for (int i = 2; i < 64; ++i) {
+                if (cnt[i - 1] >= LLONG_MAX - 1) {
+                    dp[i] = -1;
+                } else {
+                    dp[i] = (dp[i - 1] * pow(pow, (1LL << i - 1) % mdl, cnt[i - 1] + 1)) % mdl;
+                }
+            }
+            auto query = [&] (ll r) -> ll {
+                int128 res = 0;
+                ll has = 0;
+                for (int b = 62; ~b; --b) {
+                    if ((r >> b) & 1) {
+                        if (cnt[b] >= LLONG_MAX - has * (1LL << b)) {
+                            return LLONG_MAX;
+                        }
+                        res += has * (1LL << b) + cnt[b];
+                        has += 1;
+                    }
+                }
+                return min(res + popcount(r), int128(LLONG_MAX));            
+            };
+            auto calc = [&] (ll r) {
+                ll res = 0;
+                ll has = 1;
+                for (int b = 62; ~b; --b) {
+                    if ((r >> b) & 1) {
+                        if ((r >> b) & 1) {
+                            res = (res + dp[b] * pow(pow, has, cnt[b])) % mdl;
+                            has = (has * (1LL << b)) % mdl;
                         }
                     }
                 }
-    for (int i = 1; i <= n; ++i) {
-        cout << dis[i] << " \n"[i == n];
+                return (res + has) % mdl;
+            };
+            ll lt, rt;
+            ll res = 0, keep = 1;
+            {
+                ll l = 0, r = INFLL;
+                while (l < r) {
+                    ll mid = l + r >> 1;
+                    if (query(mid) > left) {
+                        r = mid;
+                    } else {
+                        l = mid + 1;
                     }
-}
+                }
+                ll rd = query(l) - left;
+                for (int b = 63; ~b and rd > 0; --b) {
+                    if ((l - 1 >> b) & 1) {
+                        rd -= 1;
+                        keep = (keep * (1LL << b)) % mdl;
+                    }
+                }
+                lt = l;
+            }
+            {
+                ll l = 0, r = INFLL;
+                while (l < r) {
+                    ll mid = l + r + 1 >> 1;
+                    if (query(mid) < right) {
+                        l = mid;
+                    } else {
+                        r = mid - 1;
+                    }
+                }
+                ll rd = right - query(l);
+                for (int b = 0; b < 63 and rd > 0; ++b) {
+                    if ((l + 1 >> b) & 1) {
+                        rd -= 1;
+                        keep = (keep * (1LL << b)) % mdl;
+                    }
+                }
+                rt = l;
+            }
+            debug(lt), debug(rt);
+            auto check = [&] (ll idx) -> bool {
+                return query(idx) >= right and query(idx - 1) < left;
+            };
+            if (not (check(lt) or check(lt - 1))) {
+                rres.push_back(((lt <= rt ? mod(calc(rt) - calc(lt - 1), mdl) : 1) * keep) % mdl);
+            } else {
+                // lt is correct
+                if (check(lt - 1)) lt -= 1;
+                ll res = 1;
+                ll d1 = left - query(lt - 1);
+                ll rem = d1 - 1;
+                int b = 0;
+                for (; b < 63 and rem > 0; ++b) {
+                    if ((lt >> b) & 1) {
+                        --rem;
+                    }
+                }
+                rem = right - left + 1;
+                for (; b < 63 and rem > 0; ++b) {
+                    if ((lt >> b) & 1) {
+                        --rem;
+                        res = (res * (1LL << b)) % mdl;
+                    }
+                }
+                rres.push_back(res);
+            }
+            // rres.push_back(int(((lt <= rt ? (calc(rt) - calc(lt - 1)) : 1) * keep) % mdl));
+        }
+        return rres;
+    }
+};
 
 int main() {
-#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
-    assert(false && "incompatible compiler variant detected.");
-#endif
-    untie, cout.tie(NULL);
-    prep();
-#ifdef SINGLE_TEST_CASE
-    solve();
-#else
-    read(int, t);
-    for (int i = 0; i < t; ++i) {
-#ifdef DUMP_TEST_CASE
-        if (t < (DUMP_TEST_CASE)) {
-            solve();
-        } else if (i + 1 == (DUMP_TEST_CASE)) {
-            dump();
-        } else {
-            dump_ignore();
-        }
-#else
-        solve();
-#endif
-    }
-#endif
+    vector<vector<long long>> queries = {{0, 2, 11}};
+    cout << Solution().findProductsOfElements(queries) << endl;
 }

src/bin/d.cc

@@ -24,13 +24,49 @@ using ull = uint64_t;
 #else
 using ll = long long;
 using ull = unsigned long long;
+using ld = long double;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
+using ld = long double;
 using pii = pair<int, int>;
 using pil = pair<int, ll>;
 using pli = pair<ll, int>;
 using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
 
 /* constants */
 constexpr int INF = 0x3f3f3f3f;
@@ -142,7 +178,9 @@ struct array_hash {
 #define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
 #define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
 #define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
 #define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
 template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
     set<T> st(__first, __last);
     size_t N = 0;
@@ -234,6 +272,7 @@ ll inverse(ll a, ll b) {
 }
 
 vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
     vector<tuple<int, int, ll>> res;
     for (int i = 2; i * i <= x; i++) {
         if (x % i == 0) {
@@ -249,6 +288,22 @@ vector<tuple<int, int, ll>> decompose(ll x) {
     return res;
 }
 
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
 /* string algorithms */
 vector<int> calc_next(string t) {  // pi function of t
   int n = (int)t.length();
@@ -327,6 +382,14 @@ template <ll mdl>
 istream& operator>>(istream& in, MLL<mdl>& num) {
     return in >> num.val;
 }
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
 /////////////////////////////////////////////////////////
 
 #define SINGLE_TEST_CASE
@@ -338,163 +401,34 @@ void dump_ignore() {}
 
 void prep() {}
 
-template<typename Addable_Info_t, typename Tag_t, typename Sequence = std::vector<Addable_Info_t>> class segtree {
-private:
-    using size_type = uint64_t;
-    using info_type = Addable_Info_t;
-    using tag_type = Tag_t;
-    size_type _max;
-    vector<info_type> d;
-    vector<tag_type> b;
-    void pull(size_type p) {
-        d[p] = d[p * 2] + d[p * 2 + 1];
-    }
-    void push(size_type p, size_type left_len, size_type right_len) {
-        d[p * 2].apply(b[p], left_len), d[p * 2 + 1].apply(b[p], right_len);
-        b[p * 2].apply(b[p]), b[p * 2 + 1].apply(b[p]);
-        b[p] = tag_type();
-    }
-    void set(size_type s, size_type t, size_type p, size_type x, const info_type& c) {
-        if (s == t) {
-            d[p] = c;
-            return;
-        }
-        size_type m = s + (t - s >> 1);
-        if (s != t) push(p, m - s + 1, t - m);
-        if (x <= m) set(s, m, p * 2, x, c);
-        else set(m + 1, t, p * 2 + 1, x, c);
-        d[p] = d[p * 2] + d[p * 2 + 1];
-    }
-    
-    void range_apply(size_type s, size_type t, size_type p, size_type l, size_type r, const tag_type& c) {
-        if (l <= s && t <= r) {
-            d[p].apply(c, t - s + 1);
-            b[p].apply(c);
-            return;
-        }
-        size_type m = s + (t - s >> 1);
-        push(p, m - s + 1, t - m);
-        if (l <= m) range_apply(s, m, p * 2, l, r, c);
-        if (r > m)  range_apply(m + 1, t, p * 2 + 1, l, r, c);
-        pull(p);
-    }
-    info_type range_query(size_type s, size_type t, size_type p, size_type l, size_type r) {
-        if (l <= s && t <= r) {
-            return d[p];
-        }
-        size_type m = s + (t - s >> 1);
-        info_type res = {};
-        push(p, m - s + 1, t - m);
-        if (l <= m) res = res + range_query(s, m, p * 2, l, r);
-        if (r > m)  res = res + range_query(m + 1, t, p * 2 + 1, l, r);
-        return res;
-    }
-    void build(const Sequence& a, size_type s, size_type t, size_type p) {
-        if (s == t) {
-            d[p] = a[s];
-            return;
-        }
-        int m = s + (t - s >> 1);
-        build(a, s, m, p * 2);
-        build(a, m + 1, t, p * 2 + 1);
-        pull(p);
-    }
-public:
-    segtree(size_type __max) : d(4 * __max), b(4 * __max), _max(__max - 1) {}
-    segtree(const Sequence& a) : segtree(a.size()) {
-        build(a, {}, _max, 1);
-    }
-    void set(size_type i, const info_type& c) {
-        set({}, _max, 1, i, c);
-    }
-    
-    void range_apply(size_type l, size_type r, const tag_type& c) {
-        range_apply({}, _max, 1, l, r, c);
-    }
-    void apply(size_type i, const tag_type& c) {
-        range_apply(i, i, c);
-    }
-    info_type range_query(size_type l, size_type r) {
-        return range_query({}, _max, 1, l, r);
-    }
-    info_type query(size_type i) {
-        return range_query(i, i);
-    }
-    Sequence serialize() {
-        Sequence res = {};
-        for (size_type i = 0; i <= _max; ++i) {
-            res.push_back(query(i));
-        }
-        return res;
-    }
-    const vector<info_type>& get_d() {
-        return d;
-    }
-};
-struct Tag {
-    ll val = 0;
-    void apply(const Tag& rhs) {
-        val = rhs.val;
-    }
-};
-struct Info {
-    ll val = 0;
-    void apply(const Tag& rhs, size_t len) {
-        val += rhs.val * len;
-    }
-};
-Info operator+(const Info &a, const Info &b) {
-    return {a.val + b.val};
-}
-
 void solve() {
-    read(int, n, q);
-    segtree<Info, Tag> a(n), b(n), c(n);
-    for (int i = 0; i < n; ++i) {
-        read(char, t);
-        int x = 0, y = 0, z = 0;
-        if (t == 'r') {
-            x = 1;
-        } else if (t == 'e') {
-            y = 1;
+    using mll = MLL<PRIME>;
+    vector<mll> pw(20);
+    pw[0] = 1;
+    for (int i = 1; i < 20; ++i) {
+        pw[i] = pw[i - 1] * 10;
+    }
+    read(int, n);
+    readvec(int, a, n);
+    array<int, 11> cnt {};
+    mll res = 0;
+    for (int i = n - 1; ~i; --i) {
+        for (int j = 1; j <= 10; ++j) {
+            res += a[i] * pw[j] * cnt[j];
+        }
+        res += mll(1) * a[i] * i;
+        int curr = 0;
+        if (a[i] == 0) {
+            curr = 1;
         } else {
-            z = 1;
+            while (a[i]) {
+                curr += 1;
+                a[i] /= 10;
             }
-        a.set(i, {x});
-        b.set(i, {y});
-        c.set(i, {z});
         }
-    while (q--) {
-        read(int, l, r);
-        --l, --r;
-        int len = (r - l + 1) / 3;
-        if (r - l + 1 < 3) {
-            cout << 0 << '\n';
-            continue;
-        }
-        int rem = (r - l + 1) % 3;
-        int res = INT_MAX;
-        int left, right;
-        unordered_set<pii, pair_hash> mp;
-        if (rem == 0) {
-            mp.emplace(0, 0);
-        } else if (rem == 1) {
-            mp.emplace(0, 0), mp.emplace(0, 1), mp.emplace(1, 0);
-        } else {
-            mp.emplace(1, 0), mp.emplace(0, 1), mp.emplace(1, 1);
-        }
-        for (auto&& [i, j] : mp) {
-            int left = l + len + i - 1;
-            int right = r - (len + j) + 1;
-            if (left >= right) continue;
-            int left_need = (left - l + 1) - a.range_query(l, left).val;
-            int right_need = (r - right + 1) - c.range_query(right, r).val;
-            int mid_need = (right - left - 1) - b.range_query(left + 1, right - 1).val;
-            // cerr << i << ' ' << j << ' ' << left_need << ' ' << mid_need << ' ' << right_need << '\n';
-            res = min(res, left_need + mid_need + right_need);
+        cnt[curr] += 1;
     }
     cout << res << '\n';
-    }
 }
 
 int main() {

src/bin/e.cc

@@ -24,13 +24,49 @@ using ull = uint64_t;
 #else
 using ll = long long;
 using ull = unsigned long long;
+using ld = long double;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
+using ld = long double;
 using pii = pair<int, int>;
 using pil = pair<int, ll>;
 using pli = pair<ll, int>;
 using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
 
 /* constants */
 constexpr int INF = 0x3f3f3f3f;
@@ -142,7 +178,9 @@ struct array_hash {
 #define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
 #define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
 #define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
 #define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
 template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
     set<T> st(__first, __last);
     size_t N = 0;
@@ -234,6 +272,7 @@ ll inverse(ll a, ll b) {
 }
 
 vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
     vector<tuple<int, int, ll>> res;
     for (int i = 2; i * i <= x; i++) {
         if (x % i == 0) {
@@ -249,6 +288,22 @@ vector<tuple<int, int, ll>> decompose(ll x) {
     return res;
 }
 
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
 /* string algorithms */
 vector<int> calc_next(string t) {  // pi function of t
   int n = (int)t.length();
@@ -327,6 +382,14 @@ template <ll mdl>
 istream& operator>>(istream& in, MLL<mdl>& num) {
     return in >> num.val;
 }
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
 /////////////////////////////////////////////////////////
 
 #define SINGLE_TEST_CASE
@@ -338,61 +401,39 @@ void dump_ignore() {}
 
 void prep() {}
 
-class quick_union {
-private:
-    vector<size_t> c, sz;
-public:
-    quick_union(size_t n) : c(n), sz(n) {
-        iota(c.begin(), c.end(), 0);
-        sz.assign(n, 1);
-    }
-    
-    size_t query(size_t i) {
-        if (c[i] != i) c[i] = query(c[i]);
-        return c[i];
-    }
-    
-    void merge(size_t i, size_t j) {
-        if (connected(i, j)) return;
-        sz[query(j)] += sz[query(i)];
-        c[query(i)] = query(j);
-    }
-    bool connected(size_t i, size_t j) {
-        return query(i) == query(j);
-    }
-    size_t query_size(size_t i) {
-        return sz[query(i)];
-    }
-};
-
 void solve() {
-    read(int, n, m);
-    quick_union qu(n + 1);
+    read(int, n);
+    readvec(string, a, n);
+    vector<pair<array<int, 26>, int>> trie(1);
+    auto insert = [&] (const string& s) -> void {
+        int curr = 0;
+        vector<int> trace;
+        for (auto&& x : s) {
+            if (not trie[curr].first[x - 97]) {
+                trie[curr].first[x - 97] = trie.size();
+                trie.push_back({});
+            }
+            curr = trie[curr].first[x - 97];
+            trace.emplace_back(curr);
+        }
+        for (auto&& i : trace) {
+            trie[i].second += 1;
+        }
+    };
+    auto query = [&] (const string& s) -> ll {
         ll res = 0;
-    vector<pair<ll, vector<int>>> data;
-    while (m--) {
-        read(int, k, c);
-        readvec(int, a, k);
-        data.emplace_back(c, a);
-    }
-    sort(data.begin(), data.end());
-    for (auto&& [c, a] : data) {
-        vector<int> o;
-        for (auto&& x : a) {
-            o.emplace_back(qu.query(x));
-        }
-        sort(o.begin(), o.end());
-        ll l = unique(o.begin(), o.end()) - o.begin();
-        res += (l - 1) * c;
-        for (int i = 1; i < l; ++i) {
-            qu.merge(o[i - 1], o[i]);
-        }
-    }
-    for (int i = 1; i <= n; ++i) {
-        if (not qu.connected(i, 1)) {
-            cout << -1 << '\n';
-            return;
+        int curr = 0;
+        for (auto&& x : s) {
+            curr = trie[curr].first[x - 97];
+            if (not curr) break;
+            res += trie[curr].second;
         }
+        return res;
+    };
+    ll res = 0;
+    for (int i = n - 1; ~i; --i) {
+        res += query(a[i]);
+        insert(a[i]);
     }
     cout << res << '\n';
 }

src/bin/f.cc

@@ -24,13 +24,49 @@ using ull = uint64_t;
 #else
 using ll = long long;
 using ull = unsigned long long;
+using ld = long double;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
+using ld = long double;
 using pii = pair<int, int>;
 using pil = pair<int, ll>;
 using pli = pair<ll, int>;
 using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
 
 /* constants */
 constexpr int INF = 0x3f3f3f3f;
@@ -142,7 +178,9 @@ struct array_hash {
 #define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
 #define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
 #define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
 #define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
 template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
     set<T> st(__first, __last);
     size_t N = 0;
@@ -234,6 +272,7 @@ ll inverse(ll a, ll b) {
 }
 
 vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
     vector<tuple<int, int, ll>> res;
     for (int i = 2; i * i <= x; i++) {
         if (x % i == 0) {
@@ -249,6 +288,22 @@ vector<tuple<int, int, ll>> decompose(ll x) {
     return res;
 }
 
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
 /* string algorithms */
 vector<int> calc_next(string t) {  // pi function of t
   int n = (int)t.length();
@@ -327,9 +382,17 @@ template <ll mdl>
 istream& operator>>(istream& in, MLL<mdl>& num) {
     return in >> num.val;
 }
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
 /////////////////////////////////////////////////////////
 
-#define SINGLE_TEST_CASE
+// #define SINGLE_TEST_CASE
 // #define DUMP_TEST_CASE 7219
 
 void dump() {}
@@ -338,91 +401,19 @@ void dump_ignore() {}
 
 void prep() {}
 
+ll calc(ll r) {
+    ll res = 0;
+    for (ll x = -r; x <= r; ++x) {
+        ll rg = (ll(ceil(sqrt((long double)(r * r) - x * x))) - 1);
+        if (rg < 0) continue;
+        else res += 2 * rg + 1;
+    }
+    return res;
+}
+
 void solve() {
-    read(int, n);
-    read(ll, l, r);
-    l = -l;
-    vector<bool> red(n + 1);
-    for (int i = 1; i <= n; ++i) {
-        read(char, c);
-        if (c == 'R') {
-            red[i] = 1;
-        }
-    }
-    adj(ch, n);
-    for (int i = 0; i < n - 1; ++i) {
-        read(int, u, v);
-        edge(ch, u, v);
-    }
-    vector<int> sz(n + 1), pos(n + 1);
-    vector<int> seq;
-    auto dfs = [&] (auto dfs, int v, int pa) -> void {
-        sz[v] = 1;
-        pos[v] = seq.size();
-        seq.emplace_back(v);
-        for (auto&& u : ch[v]) {
-            if (u == pa) continue;
-            dfs(dfs, u, v);
-            sz[v] += sz[u];
-        }
-    };
-    dfs(dfs, 1, 0);
-    vector<int> res(n + 1);
-    auto dfs1 = [&] (auto dfs1, int v, int pa) -> int {
-        int ignore = 0;
-        for (auto&& u : ch[v]) {
-            if (u == pa) continue;
-            ignore += dfs1(dfs1, u, v);
-        }
-        if (red[v]) {
-            int m = sz[v] - ignore;
-            ll mx = 0;
-            for (int i = 0; i <= m; ++i) {
-                ll curr = min(ll(1) * l * (m - i), ll(1) * r * i);
-                if (curr > mx) {
-                    mx = curr;
-                }
-            }
-            ll tot = 0;
-            int f = 1;
-            for (int j = 0; j < sz[v]; ++j) {
-                int i = pos[v] + j;
-                if (red[seq[i]] and seq[i] != v) {
-                    j += sz[seq[i]] - 1;
-                    continue;
-                }
-                if (f) {
-                    ll use = min(r, mx - tot);
-                    res[seq[i]] = use;
-                    tot += use;
-                    if (tot == mx) {
-                        f = 0;
-                    }
-                } else {
-                    ll use = min(tot, l);
-                    res[seq[i]] = -use;
-                    tot -= use;
-                }
-            }
-            return sz[v];
-        } else {
-            return ignore;
-        }
-    };
-    dfs1(dfs1, 1, 0);
-    if (not red[1]) {
-        for (int j = 0; j < sz[1]; ++j) {
-            int i = pos[1] + j;
-            if (red[seq[i]] and seq[i] != 1) {
-                j += sz[seq[i]] - 1;
-                continue;
-            }
-            res[seq[i]] = l > r ? (-l) : r;
-        }
-    }
-    for (int i = 1; i <= n; ++i) {
-        cout << res[i] << " \n"[i == n];
-    }
+    read(ll, r);
+    cout << calc(r + 1) - calc(r) << '\n';
 }
 
 int main() {

src/bin/g.cc

@@ -24,13 +24,49 @@ using ull = uint64_t;
 #else
 using ll = long long;
 using ull = unsigned long long;
+using ld = long double;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
+using ld = long double;
 using pii = pair<int, int>;
 using pil = pair<int, ll>;
 using pli = pair<ll, int>;
 using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
 
 /* constants */
 constexpr int INF = 0x3f3f3f3f;
@@ -142,7 +178,9 @@ struct array_hash {
 #define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
 #define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
 #define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
 #define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
 template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
     set<T> st(__first, __last);
     size_t N = 0;
@@ -234,6 +272,7 @@ ll inverse(ll a, ll b) {
 }
 
 vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
     vector<tuple<int, int, ll>> res;
     for (int i = 2; i * i <= x; i++) {
         if (x % i == 0) {
@@ -249,6 +288,22 @@ vector<tuple<int, int, ll>> decompose(ll x) {
     return res;
 }
 
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
 /* string algorithms */
 vector<int> calc_next(string t) {  // pi function of t
   int n = (int)t.length();
@@ -327,6 +382,14 @@ template <ll mdl>
 istream& operator>>(istream& in, MLL<mdl>& num) {
     return in >> num.val;
 }
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
 /////////////////////////////////////////////////////////
 
 #define SINGLE_TEST_CASE
@@ -336,37 +399,135 @@ void dump() {}
 
 void dump_ignore() {}
 
-constexpr int MAXN = 3e5 + 10;
-using mll = MLL<PRIME>;
-mll fact[MAXN];
-void prep() {
-    fact[0] = 1;
-    for (int i = 1; i < MAXN; ++i) {
-        fact[i] = fact[i - 1] * i;
+void prep() {}
+
+template<typename Addable_Info_t, typename Tag_t, typename Sequence = std::vector<Addable_Info_t>> class segtree {
+private:
+    using size_type = uint64_t;
+    using info_type = Addable_Info_t;
+    using tag_type = Tag_t;
+    size_type _max;
+    vector<info_type> d;
+    vector<tag_type> b;
+    void pull(size_type p) {
+        d[p] = d[p * 2] + d[p * 2 + 1];
     }
+    void push(size_type p, size_type left_len, size_type right_len) {
+        d[p * 2].apply(b[p], left_len), d[p * 2 + 1].apply(b[p], right_len);
+        b[p * 2].apply(b[p]), b[p * 2 + 1].apply(b[p]);
+        b[p] = tag_type();
+    }
+    void set(size_type s, size_type t, size_type p, size_type x, const info_type& c) {
+        if (s == t) {
+            d[p] = c;
+            return;
+        }
+        size_type m = s + (t - s >> 1);
+        if (s != t) push(p, m - s + 1, t - m);
+        if (x <= m) set(s, m, p * 2, x, c);
+        else set(m + 1, t, p * 2 + 1, x, c);
+        d[p] = d[p * 2] + d[p * 2 + 1];
+    }
+    
+    void range_apply(size_type s, size_type t, size_type p, size_type l, size_type r, const tag_type& c) {
+        if (l <= s && t <= r) {
+            d[p].apply(c, t - s + 1);
+            b[p].apply(c);
+            return;
+        }
+        size_type m = s + (t - s >> 1);
+        push(p, m - s + 1, t - m);
+        if (l <= m) range_apply(s, m, p * 2, l, r, c);
+        if (r > m)  range_apply(m + 1, t, p * 2 + 1, l, r, c);
+        pull(p);
+    }
+    info_type range_query(size_type s, size_type t, size_type p, size_type l, size_type r) {
+        if (l <= s && t <= r) {
+            return d[p];
+        }
+        size_type m = s + (t - s >> 1);
+        info_type res = {};
+        push(p, m - s + 1, t - m);
+        if (l <= m) res = res + range_query(s, m, p * 2, l, r);
+        if (r > m)  res = res + range_query(m + 1, t, p * 2 + 1, l, r);
+        return res;
+    }
+    void build(const Sequence& a, size_type s, size_type t, size_type p) {
+        if (s == t) {
+            d[p] = a[s];
+            return;
+        }
+        int m = s + (t - s >> 1);
+        build(a, s, m, p * 2);
+        build(a, m + 1, t, p * 2 + 1);
+        pull(p);
+    }
+public:
+    segtree(size_type __max) : d(4 * __max), b(4 * __max), _max(__max - 1) {}
+    segtree(const Sequence& a) : segtree(a.size()) {
+        build(a, {}, _max, 1);
+    }
+    void set(size_type i, const info_type& c) {
+        set({}, _max, 1, i, c);
+    }
+    
+    void range_apply(size_type l, size_type r, const tag_type& c) {
+        range_apply({}, _max, 1, l, r, c);
+    }
+    void apply(size_type i, const tag_type& c) {
+        range_apply(i, i, c);
+    }
+    info_type range_query(size_type l, size_type r) {
+        return range_query({}, _max, 1, l, r);
+    }
+    info_type query(size_type i) {
+        return range_query(i, i);
+    }
+    Sequence serialize() {
+        Sequence res = {};
+        for (size_type i = 0; i <= _max; ++i) {
+            res.push_back(query(i));
+        }
+        return res;
+    }
+    const vector<info_type>& get_d() {
+        return d;
+    }
+};
+struct Tag {
+    ll val = -1;
+    void apply(const Tag& rhs) {
+        if (rhs.val != -1)
+        val = rhs.val;
+    }
+};
+struct Info {
+    ll val = -INFLL;
+    void apply(const Tag& rhs, size_t len) {
+        if (rhs.val != -1)
+        val = rhs.val * len;
+    }
+};
+Info operator+(const Info &a, const Info &b) {
+    return {max(a.val, b.val)};
 }
 
 void solve() {
-    using mll = MLL<PRIME>;
-    auto comb = [&] (int n, int k) -> mll {
-        return fact[n] / fact[k];
-    };
+    read(int, m);
+    read(ll, c);
     read(int, n);
-    vector<int> a(n);
-    int m = 0;
+    vector<pil> a(n);
     for (int i = 0; i < n; ++i) {
-        cin >> a[i];
-        m += a[i];
+        cin >> a[i].first >> a[i].second;
     }
-    vector<vector<int>> dp(n + 1, vector<int>(n + 1));
-    for (int i = 1; i <= n; ++i) {
-        for (int j = 1; j <= n; ++j) {
-            dp[i][j] = (a[i - 1] != 0 ? dp[i - 1][j - 1] + a[i - 1] : 0) + dp[i - 1][j];
-        }
-    }
-    mll res = 0;
-    for (int i = n; ~i; --i) {
-        res = 1 + (m - dp[n][i] / comb(n, i)) / (m - i) * res;
+    segtree<Info, Tag> tr1(m + 1), tr2(m + 1);
+    ll res = 0;
+    for (int i = n - 1; ~i; --i) {
+        ll dp = max(a[i].second + max(ll(0), -c * a[i].first + tr1.range_query(1, a[i].first).val),
+                    a[i].second + max(ll(0), a[i].first == m ? 0 : (c * a[i].first + tr2.range_query(a[i].first + 1, m).val)));
+        res = max(res, dp - c * (a[i].first - 1));
+        tr1.set(a[i].first, {max(tr1.query(a[i].first).val, dp + c * a[i].first)});
+        tr2.set(a[i].first, {max(tr2.query(a[i].first).val, dp - c * a[i].first)});
     }
     cout << res << '\n';
 }

src/bin/h.cc

@@ -0,0 +1,438 @@
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+void solve() {
+    read(int, n);
+    vector<vector<int>> g(3, vector<int>(n));
+    for (int i = 0; i < 3; ++i) {
+        for (int j = 0; j < n; ++j) {
+            cin >> g[i][j];
+        }
+    }
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/lg-p4782.cc

@@ -0,0 +1,553 @@
+// #pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
+using namespace std;
+
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
+    return res;
+}
+
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
+        }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+
+namespace tarjan {
+    struct mutex_cond {
+        int v1; bool cond1;
+        int v2; bool cond2;
+        mutex_cond(int v1, bool cond1, int v2, bool cond2) : v1(v1), cond1(cond1), v2(v2), cond2(cond2) {}
+    };
+    struct inclusive_cond {
+        int v1; bool cond1;
+        int v2; bool cond2;
+        inclusive_cond(int v1, bool cond1, int v2, bool cond2) : v1(v1), cond1(cond1), v2(v2), cond2(cond2) {}
+    };
+    // Returns the mapping between vertices and their affiliated sccs.
+    vector<int> scc(const vector<vector<int>>& ch) {
+        int n = ch.size();
+        int cnt = 0, scn = 0;
+        vector<int> dfn(n), low(n), vis(n), st;
+        vector<int> br(n);
+        auto tarjan = [&] (auto tarjan, int v) -> void {
+            dfn[v]=low[v]=++cnt;
+            st.push_back(v);
+            vis[v]=1;
+            for(const auto&u:ch[v])
+                if(!dfn[u]) tarjan(tarjan, u),low[v]=min(low[v],low[u]);
+                else if(vis[u])low[v]=min(low[v],dfn[u]);
+            if(dfn[v]==low[v]){
+                ++scn;
+                int u;
+                do u=st.back(), st.pop_back(),vis[u]=0,br[u]=scn; while(u!=v);
+            }
+        };
+        for (int i = 0; i < n; ++i) {
+            if (!dfn[i]) {
+                tarjan(tarjan, i);
+            }
+        }
+        return br;
+    }
+    // This method can eliminate redundant edges or self-loops
+    vector<vector<int>> build_scc(const vector<vector<int>>& ch) {
+        int n = ch.size();
+        auto br = scc(ch);
+        int cnt = *max_element(br.begin(), br.end());
+        vector<unordered_set<int, safe_hash>> rb(cnt + 1);
+        for (int i = 0; i < n; ++i) {
+            for (auto&& u : ch[i]) {
+                if (br[i] != br[u]) rb[br[i]].emplace(br[u]);
+            }
+        }
+        vector<vector<int>> res(cnt + 1);
+        for (int i = 1; i <= cnt; ++i) {
+            res[i] = vector<int>(rb[i].begin(), rb[i].end());
+        }
+        return res;
+    }
+    
+    // This method can eliminate redundant edges or self-loops
+    // return form: (scc size, children of scc)
+    vector<pair<size_t, vector<int>>> build_scc_with_size(const vector<vector<int>>& ch) {
+        int n = ch.size();
+        auto br = scc(ch);
+        int cnt = *max_element(br.begin(), br.end());
+        vector<unordered_set<int, safe_hash>> rb(cnt + 1);
+        for (int i = 0; i < n; ++i) {
+            for (auto&& u : ch[i]) {
+                if (br[i] != br[u]) rb[br[i]].emplace(br[u]);
+            }
+        }
+        vector<pair<size_t, vector<int>>> res(cnt + 1);
+        for (int i = 1; i <= cnt; ++i) {
+            res[i].second = vector<int>(rb[i].begin(), rb[i].end());
+        }
+        for (int i = 1; i <= n; ++i) {
+            res[br[i]].first += 1;
+        }
+        return res;
+    }
+    // indices start from 1, result has `n` items
+    optional<vector<bool>> solve_twosat(int n, const vector<mutex_cond>& conditions) {
+        vector<vector<int>> ch(2 * n + 1);
+        for (auto&& [v1, cond1, v2, cond2] : conditions) {
+            ch[(1 ^ cond1) * n + v1].emplace_back(cond2 * n + v2);
+            ch[(1 ^ cond2) * n + v2].emplace_back(cond1 * n + v1);
+        }
+        auto sccno = scc(ch);
+        for (int i = 1; i <= n; ++i) {
+            if (sccno[i] == sccno[i + n]) {
+                return nullopt;
+            }
+        }
+        vector<bool> res;
+        for (int i = 1; i <= n; ++i) {
+            if (sccno[i] < sccno[i + n]) {
+                res.emplace_back(false);
+            } else {
+                res.emplace_back(true);
+            }
+        }
+        return res;
+    };
+    // indices start from 1, result has `n` items
+    optional<vector<bool>> solve_twosat(int n, const vector<inclusive_cond>& conditions) {
+        vector<mutex_cond> trans_conds;
+        for (auto&& [v1, cond1, v2, cond2] : conditions) {
+            trans_conds.emplace_back(v1, cond1, v2, not cond2);
+        }
+        return solve_twosat(n, trans_conds);
+    }
+}
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+void solve() {
+    read(int, n, m);
+    vector<tarjan::mutex_cond> conditions;
+    for (int i = 0; i < m; ++i) {
+        read(int, x, a, y, b);
+        conditions.emplace_back(x, a, y, b);
+    }
+    auto sol = tarjan::solve_twosat(n, conditions);
+    if (not sol.has_value()) {
+        cout << "IMPOSSIBLE\n";
+    } else {
+        cout << "POSSIBLE\n";
+        putvec(sol.value());
+    }
+}
+
+int main() {
+#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
+    assert(false && "incompatible compiler variant detected.");
+#endif
+    untie, cout.tie(NULL);
+    prep();
+#ifdef SINGLE_TEST_CASE
+    solve();
+#else
+    read(int, t);
+    for (int i = 0; i < t; ++i) {
+#ifdef DUMP_TEST_CASE
+        if (t < (DUMP_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/std.in

@@ -1,6 +1,17 @@
-3 3
-1 2 1
-2 3 1
-1 3 1
-30 10 20
-
+50 10
+15
+37 261
+28 404
+49 582
+19 573
+18 633
+3 332
+31 213
+30 377
+50 783
+17 798
+4 561
+41 871
+15 525
+16 444
+26 453

src/bin/template.cc

@@ -28,10 +28,43 @@ using ld = long double;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
+using ld = long double;
 using pii = pair<int, int>;
 using pil = pair<int, ll>;
 using pli = pair<ll, int>;
 using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
 template <typename T> using max_heap = priority_queue<T>;
 template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
 
@@ -145,7 +178,9 @@ struct array_hash {
 #define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
 #define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
 #define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
 #define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
 template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
     set<T> st(__first, __last);
     size_t N = 0;
@@ -347,6 +382,14 @@ template <ll mdl>
 istream& operator>>(istream& in, MLL<mdl>& num) {
     return in >> num.val;
 }
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
 /////////////////////////////////////////////////////////
 
 #define SINGLE_TEST_CASE

src/bin/test.cc

@@ -1,15 +1,530 @@
-#include <bits/stdc++.h>
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * Useful Macros
+ *   by subcrip
+ * (requires C++17)
+ */
+
+#include<bits/stdc++.h>
 using namespace std;
 
-vector<int> effect() {
-    cerr << "called.\n";
-    vector<int> res(5);
-    iota(res.begin(), res.end(), 0);
+/* macro helpers */
+#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
+#define __DECOMPOSE_S(a, x) auto x = a;
+#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
+constexpr void __() {}
+#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
+#define __as_typeof(container) decltype(container)::value_type
+
+/* type aliases */
+#if LONG_LONG_MAX != INT64_MAX
+using ll = int64_t;
+using ull = uint64_t;
+#else
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = long double;
+using pii = pair<int, int>;
+using pil = pair<int, ll>;
+using pli = pair<ll, int>;
+using pll = pair<ll, ll>;
+using pid = pair<int, ld>;
+using pdi = pair<ld, int>;
+using pld = pair<ll, ld>;
+using pdl = pair<ld, ll>;
+using pdd = pair<ld, ld>;
+using tlll = tuple<ll, ll, ll>;
+using tlld = tuple<ll, ll, ld>;
+using tlli = tuple<ll, ll, int>;
+using tldl = tuple<ll, ld, ll>;
+using tldd = tuple<ll, ld, ld>;
+using tldi = tuple<ll, ld, int>;
+using tlil = tuple<ll, int, ll>;
+using tlid = tuple<ll, int, ld>;
+using tlii = tuple<ll, int, int>;
+using tdll = tuple<ld, ll, ll>;
+using tdld = tuple<ld, ll, ld>;
+using tdli = tuple<ld, ll, int>;
+using tddl = tuple<ld, ld, ll>;
+using tddd = tuple<ld, ld, ld>;
+using tddi = tuple<ld, ld, int>;
+using tdil = tuple<ld, int, ll>;
+using tdid = tuple<ld, int, ld>;
+using tdii = tuple<ld, int, int>;
+using till = tuple<int, ll, ll>;
+using tild = tuple<int, ll, ld>;
+using tili = tuple<int, ll, int>;
+using tidl = tuple<int, ld, ll>;
+using tidd = tuple<int, ld, ld>;
+using tidi = tuple<int, ld, int>;
+using tiil = tuple<int, int, ll>;
+using tiid = tuple<int, int, ld>;
+using tiii = tuple<int, int, int>;
+template <typename T> using max_heap = priority_queue<T>;
+template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
+
+/* constants */
+constexpr int INF = 0x3f3f3f3f;
+constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
+constexpr ll MDL = 1e9 + 7;
+constexpr ll PRIME = 998'244'353;
+constexpr ll MDL1 = 8784491;
+constexpr ll MDL2 = PRIME;
+constexpr int128 INT128_MAX = numeric_limits<int128>::max();
+constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
+constexpr int128 INT128_MIN = numeric_limits<int128>::min();
+constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
+
+/* random */
+
+mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
+
+/* bit-wise operations */
+#define lowbit(x) ((x) & -(x))
+#define popcount(x) (__builtin_popcountll(ll(x)))
+#define parity(x) (__builtin_parityll(ll(x)))
+#define msp(x) (63LL - __builtin_clzll(ll(x)))
+#define lsp(x) (__builtin_ctzll(ll(x)))
+
+/* arithmetic operations */
+#define mod(x, y) ((((x) % (y)) + (y)) % (y))
+
+/* fast pairs */
+#define upair ull
+#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
+#define u1(p) ((p) >> 32)
+#define u2(p) ((p) & ((1ULL << 32) - 1))
+#define ult std::less<upair>
+#define ugt std::greater<upair>
+
+#define ipair ull
+#define imake(x, y) (umake(x, y))
+#define i1(p) (int(u1(ll(p))))
+#define i2(p) (ll(u2(p) << 32) >> 32)
+struct ilt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) < i2(b);
+        else return i1(a) < i1(b);
+    }
+};
+struct igt {
+    bool operator()(const ipair& a, const ipair& b) const {
+        if (i1(a) == i1(b)) return i2(a) > i2(b);
+        else return i1(a) > i1(b);
+    }
+};
+
+/* conditions */
+#define loop while (1)
+#define if_or(var, val) if (!(var == val)) var = val; else
+#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
+#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
+
+/* hash */
+struct safe_hash {
+    // https://codeforces.com/blog/entry/62393
+    static uint64_t splitmix64(uint64_t x) {
+        // http://xorshift.di.unimi.it/splitmix64.c
+        x += 0x9e3779b97f4a7c15;
+        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+        return x ^ (x >> 31);
+    }
+
+    size_t operator()(uint64_t x) const {
+        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
+        return splitmix64(x + FIXED_RANDOM);
+    }
+};
+
+struct pair_hash {
+    template <typename T, typename U>
+    size_t operator()(const pair<T, U>& a) const {
+        auto hash1 = safe_hash()(a.first);
+        auto hash2 = safe_hash()(a.second);
+        if (hash1 != hash2) {
+            return hash1 ^ hash2;
+        }
+        return hash1;
+    }
+};
+
+uniform_int_distribution<mt19937::result_type> dist(PRIME);
+const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
+struct array_hash {
+    template <typename Sequence>
+    size_t operator()(const Sequence& arr) const {
+        size_t pw1 = 1, pw2 = 1;
+        size_t res1 = 0, res2 = 0;
+        for (auto&& x : arr) {
+            res1 = (res1 + x * pw1) % __array_hash_mdl1;
+            res2 = (res2 + x * pw2) % __array_hash_mdl2;
+            pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
+            pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
+        }
+        return res1 + res2;
+    }
+};
+
+/* build data structures */
+#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
+#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
+#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
+#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
+#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
+#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
+#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
+template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    map<T, size_t> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
+    set<T> st(__first, __last);
+    size_t N = 0;
+    unordered_map<T, size_t, safe_hash> mp;
+    for (auto&& x : st) mp[x] = ++N;
+    return {N, mp};
+}
+
+/* io */
+#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+template<typename T> void __read(T& x) { cin >> x; }
+template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
+#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
+#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
+#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
+template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
+    out << "{" << p.first << ", " << p.second << "}";
+    return out;
+}
+template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
+void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
+    using swallow = int[]; // guaranties left to right order
+    (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
+}
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
+    os << "{";
+    print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
+    return os << "}";
+}
+template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
+    for (auto&& i : vec) out << i << ' ';
+    return out;
+}
+std::ostream& operator<<(std::ostream& dest, const int128& value) {
+    // https://stackoverflow.com/a/25115163/23881100
+    std::ostream::sentry s( dest );
+    if ( s ) {
+        uint128 tmp = value < 0 ? -value : value;
+        char buffer[ 128 ];
+        char* d = std::end( buffer );
+        do {
+            -- d;
+            *d = "0123456789"[ tmp % 10 ];
+            tmp /= 10;
+        } while ( tmp != 0 );
+        if ( value < 0 ) {
+            -- d;
+            *d = '-';
+        }
+        int len = std::end( buffer ) - d;
+        if ( dest.rdbuf()->sputn( d, len ) != len ) {
+            dest.setstate( std::ios_base::badbit );
+        }
+    }
+    return dest;
+}
+
+/* pops */
+#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
+#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
+#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
+
+/* math */
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+void __exgcd(ll a, ll b, ll& x, ll& y) {
+  if (b == 0) {
+    x = 1, y = 0;
+    return;
+  }
+  __exgcd(b, a % b, y, x);
+  y -= a / b * x;
+}
+
+ll inverse(ll a, ll b) {
+    ll x, y;
+    __exgcd(a, b, x, y);
+    return mod(x, b);
+}
+
+vector<tuple<int, int, ll>> decompose(ll x) {
+    // return (factor, count, factor ** count)
+    vector<tuple<int, int, ll>> res;
+    for (int i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+            ll pw = 1;
+            while (x % i == 0) ++cnt, x /= i, pw *= i;
+            res.emplace_back(i, cnt, pw);
+        }
+    }
+    if (x != 1) {
+        res.emplace_back(x, 1, x);
+    }
     return res;
 }
 
-int main() {
-    for (auto&& i : effect()) {
-        cout << i << '\n';
+vector<pii> decompose_prime(int N) {
+    // return (factor, count)
+    vector<pii> result;
+    for (int i = 2; i * i <= N; i++) {
+        if (N % i == 0) {
+            int cnt = 0;
+            while (N % i == 0) N /= i, ++cnt;
+            result.emplace_back(i, cnt);
         }
+    }
+    if (N != 1) {
+        result.emplace_back(N, 1);
+    }
+    return result;
+}
+
+/* string algorithms */
+vector<int> calc_next(string t) {  // pi function of t
+  int n = (int)t.length();
+  vector<int> pi(n);
+  for (int i = 1; i < n; i++) {
+    int j = pi[i - 1];
+    while (j > 0 && t[i] != t[j]) j = pi[j - 1];
+    if (t[i] == t[j]) j++;
+    pi[i] = j;
+  }
+  return pi;
+}
+vector<int> calc_z(string t) {  // z function of t
+    int m = t.length();
+    vector<int> z;
+    z.push_back(m);
+    pair<int, int> prev = {1, -1};
+    for (int i = 1; i < m; ++i) {
+        if (z[i - prev.first] + i <= prev.second) {
+            z.push_back(z[i - prev.first]);
+        } else {
+            int j = max(i, prev.second + 1);
+            while (j < m && t[j] == t[j - i]) ++j;
+            z.push_back(j - i);
+            prev = {i, j - 1};
+        }
+    }
+    return z;
+}
+vector<int> kmp(string s, string t) {  // find all t in s
+  string cur = t + '#' + s;
+  int sz1 = s.size(), sz2 = t.size();
+  vector<int> v;
+  vector<int> lps = calc_next(cur);
+  for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
+    if (lps[i] == sz2) v.push_back(i - 2 * sz2);
+  }
+  return v;
+}
+int period(string s) {  // find the length of shortest recurring period
+    int n = s.length();
+    auto z = calc_z(s);
+    for (int i = 1; i <= n / 2; ++i) {
+        if (n % i == 0 && z[i] == n - i) {
+            return i;
+        }
+    }
+    return n;
+}
+
+/* modular arithmetic */
+template <ll mdl> struct MLL {
+    ll val;
+    MLL(ll v = 0) : val(mod(v, mdl)) {}
+    MLL(const MLL<mdl>& other) : val(other.val) {}
+    friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
+    friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
+    friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
+    friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
+    friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
+}
+template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
+    std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
+}
+/////////////////////////////////////////////////////////
+
+class Solution {
+public:
+    vector<int> findProductsOfElements(vector<vector<long long>>& queries) {
+        vector<int> rres;
+        for (auto&& v : queries) {
+            ll left = v[0] + 1, right = v[1] + 1, mdl = v[2];
+            vector<ll> dp(64);
+            vector<ll> cnt(64);
+            dp[1] = 1;
+            cnt[1] = 1;
+            for (int i = 2; i < 64; ++i) {
+                if (cnt[i - 1] > LLONG_MAX / 3) {
+                    cnt[i] = LLONG_MAX;
+                } else {
+                    cnt[i] = cnt[i - 1] * 3 + 1;
+                }
+            }
+            unordered_map<ll, ll, safe_hash> cache;
+            cache[0] = 1;
+            auto pow = [&] (auto pow, ll b, ll m) -> ll {
+                if (cache[m]) return cache[m];
+                ll curr = pow(pow, b, m / 2);
+                cache[m] = ((((curr * curr) % mdl) * ((m & 1) ? (b % mdl) : 1)) % mdl);
+                return cache[m];
+            };
+            for (int i = 2; i < 64; ++i) {
+                if (cnt[i - 1] >= LLONG_MAX - 1) {
+                    dp[i] = -1;
+                } else {
+                    dp[i] = (dp[i - 1] * pow(pow, (1LL << i - 1) % mdl, cnt[i - 1] + 1)) % mdl;
+                }
+            }
+            auto query = [&] (ll r) -> ll {
+                int128 res = 0;
+                ll has = 0;
+                for (int b = 62; ~b; --b) {
+                    if ((r >> b) & 1) {
+                        if (cnt[b] >= LLONG_MAX - has * (1LL << b)) {
+                            return LLONG_MAX;
+                        }
+                        res += has * (1LL << b) + cnt[b];
+                        has += 1;
+                    }
+                }
+                return min(res + popcount(r), int128(LLONG_MAX));            
+            };
+            auto calc = [&] (ll r) {
+                ll res = 0;
+                ll has = 1;
+                for (int b = 62; ~b; --b) {
+                    if ((r >> b) & 1) {
+                        if ((r >> b) & 1) {
+                            res = (res + dp[b] * pow(pow, has, cnt[b])) % mdl;
+                            has = (has * (1LL << b)) % mdl;
+                        }
+                    }
+                }
+                return (res + has) % mdl;
+            };
+            ll lt, rt;
+            ll res = 0, keep = 1;
+            {
+                ll l = 0, r = INFLL;
+                while (l < r) {
+                    ll mid = l + r >> 1;
+                    if (query(mid) > left) {
+                        r = mid;
+                    } else {
+                        l = mid + 1;
+                    }
+                }
+                ll rd = query(l) - left;
+                for (int b = 63; ~b and rd > 0; --b) {
+                    if ((l - 1 >> b) & 1) {
+                        rd -= 1;
+                        keep = (keep * (1LL << b)) % mdl;
+                    }
+                }
+                lt = l;
+            }
+            {
+                ll l = 0, r = INFLL;
+                while (l < r) {
+                    ll mid = l + r + 1 >> 1;
+                    if (query(mid) < right) {
+                        l = mid;
+                    } else {
+                        r = mid - 1;
+                    }
+                }
+                ll rd = right - query(l);
+                for (int b = 0; b < 63 and rd > 0; ++b) {
+                    if ((l + 1 >> b) & 1) {
+                        rd -= 1;
+                        keep = (keep * (1LL << b)) % mdl;
+                    }
+                }
+                rt = l;
+            }
+            debug(lt), debug(rt);
+            auto check = [&] (ll idx) -> bool {
+                return query(idx) >= right and query(idx - 1) < left;
+            };
+            if (not (check(lt) or check(lt - 1))) {
+                rres.push_back(((lt <= rt ? mod(calc(rt) - calc(lt - 1), mdl) : 1) * keep) % mdl);
+            } else {
+                // lt is correct
+                if (check(lt - 1)) lt -= 1;
+                ll res = 1;
+                ll d1 = left - query(lt - 1);
+                ll rem = d1 - 1;
+                int b = 0;
+                for (; b < 63 and rem > 0; ++b) {
+                    if ((lt >> b) & 1) {
+                        --rem;
+                    }
+                }
+                rem = right - left + 1;
+                for (; b < 63 and rem > 0; ++b) {
+                    if ((lt >> b) & 1) {
+                        --rem;
+                        res = (res * (1LL << b)) % mdl;
+                    }
+                }
+                rres.push_back(res);
+            }
+            // rres.push_back(int(((lt <= rt ? (calc(rt) - calc(lt - 1)) : 1) * keep) % mdl));
+        }
+        return rres;
+    }
+};
+
+int main() {
+    vector<vector<long long>> queries = {{0, 2, 11}};
+    cout << Solution().findProductsOfElements(queries) << endl;
 }

src/bin/test.py

@@ -1,31 +1,51 @@
-from itertools import pairwise
-from random import shuffle, randint
-from os import system
+# void solve() {
+#     read(ll, n, k, q);
+#     vector<ll> a(k + 1), b(k + 1);
+#     for (int i = 1; i <= k; ++i) cin >> a[i];
+#     for (int i = 1; i <= k; ++i) cin >> b[i];
+#     while (q--) {
+#         read(ll, d);
+#         int l = 0, r = k;
+#         while (l < r) {
+#             int mid = l + r + 1 >> 1;
+#             if (a[mid] <= d) {
+#                 l = mid;
+#             } else {
+#                 r = mid - 1;
+#             }
+#         }
+#         
+#         if (a[l] == d) {
+#             cout << b[l] << ' ';
+#         } else {
+#             ll res = double(1) * (d - a[l]) / (a[l + 1] - a[l]) * (b[l + 1] - b[l]);
+#             cout << b[l] + res << ' ';
+#         }
+#     }
+#     cout << endl;
+# }
 
-def gen_tree(n):
-    tree = ''
-    for i in range(2, n + 1):
-        fa = randint(1, i - 1)
-        tree += f'{fa} {i}\n'
-    return tree
-
-N = 10_000_000
-prime = []
-is_prime = [False] * N
-
-def Eratosthenes(n):
-    is_prime[0] = is_prime[1] = False
-    for i in range(2, n + 1):
-        is_prime[i] = True
-    for i in range(2, n + 1):
-        if is_prime[i]:
-            prime.append(i)
-            if i * i > n:
-                continue
-            for j in range(i * i, n + 1, i):
-                is_prime[j] = False
-
-if __name__ == '__main__':
-    print(1)
-    print(1000000)
-    print('8 6 ' * 500000)
+import sys
+input = sys.stdin.readline
+t = int(input())
+for _ in range(t):
+    n = int(input())
+    k = int(input())
+    q = int(input())
+    a = [0] * (k + 1)
+    b = [0] * (k + 1)
+    for _ in range(q):
+        d = int(input())
+        l = 0
+        r = k
+        while l < r:
+            mid = l + r + 1 >> 1
+            if a[mid] <= d:
+                l = mid
+            else:
+                r = mid - 1
+        if a[l] == d:
+            print(b[l], end=' ')
+        else:
+            res = (d - a[l]) / (a[l + 1] - a[l]) * (b[l + 1] - b[l])
+            print(b[l] + res)