backup

src/bin/at-arc178a.cc

@@ -0,0 +1,550 @@
+/**
+ * Author:   subcrip
+ * Created:  2024-05-30 10:30:13
+ * Modified: 2024-05-30 10:41:55
+ * Elapsed:  11 minutes
+ */
+
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * This code should require C++14.
+ * However, it's only been tested with 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) remove_reference<decltype(container)>::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<>>;
+template <typename T> using oi = ostream_iterator<T>;
+template <typename T> using ii = istream_iterator<T>;
+
+/* 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 (auto& x : a) cin >> x;)
+#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
+#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#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> istream& operator>>(istream& in, pair<T, U>& p) {
+    return in >> p.first >> p.second;
+}
+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 */
+template <typename return_t>
+return_t qpow(ll b, ll p) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    return_t half = qpow<return_t>(b, p / 2);
+    if (p % 2 == 1) return half * half * b;
+    else return half * half;
+}
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+
+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; }
+};
+struct MLLd {
+    ll val, mdl;
+    MLLd(ll mdl, ll v = 0) : mdl(mdl), val(mod(v, mdl)) {}
+    MLLd(const MLLd& other) : mdl(other.mdl), val(other.val) {}
+    friend MLLd operator+(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val + rhs.val, lhs.mdl)); }
+    friend MLLd operator-(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - rhs.val, lhs.mdl)); }
+    friend MLLd operator*(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * rhs.val, lhs.mdl)); }
+    friend MLLd operator/(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * mod(inverse(rhs.val, lhs.mdl), lhs.mdl), lhs.mdl)); }
+    friend MLLd operator%(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - (lhs / rhs).val, lhs.mdl)); }
+    friend bool operator==(const MLLd& lhs, const MLLd& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLLd& lhs, const MLLd& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLLd& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLLd& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLLd& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLLd& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLLd& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+ostream& operator<<(ostream& out, const MLLd& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+istream& operator>>(istream& in, MLLd& 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)); });
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
+    vector<pair<T, U>> res;
+    auto a_it = a_first;
+    auto b_it = b_first;
+    for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
+        res.emplace_back(*a_it, *b_it);
+    }
+    return res;
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
+    vector<pair<T, U>> res;
+    if (n > 0) {
+        res.emplace_back(*a_first, *b_first);
+        for (size_t i = 1; i != n; ++i) {
+            res.emplace_back(*++a_first, *++b_first);
+        }
+    }
+    return res;
+}
+template <typename T>
+class ArithmeticIterator : bidirectional_iterator_tag {
+public:
+    using difference_type = ptrdiff_t;
+    using value_type = T;
+private:
+    value_type value;
+public:
+    ArithmeticIterator(const T& value) : value(value) {}
+    value_type operator*() const { return value; }
+    ArithmeticIterator<T>& operator++() { ++value; return *this; }
+    ArithmeticIterator<T>& operator--() { --value; return *this; }
+    bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
+};
+template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
+    return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
+}
+/////////////////////////////////////////////////////////
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+void solve() {
+    read(int, n, m);
+    vector<bool> mark(n + 1);
+    while (m--) {
+        read(int, x);
+        mark[x] = 1;
+    }
+    vector<int> res;
+    int cand = 0;
+    if (mark[1]) {
+        cout << -1 << '\n';
+        return;
+    }
+    for (int i = 1; i <= n; ++i) {
+        if (mark[i] and not mark[i - 1]) {
+            cand = i;
+        } else {
+            res.emplace_back(i);
+        }
+        if (not mark[i] and cand) {
+            res.emplace_back(cand);
+            cand = 0;
+        }
+    }
+    if (cand) {
+        cout << -1 << '\n';
+        return;
+    }
+    putvec(res);
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not 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 != (TOT_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1635e.cc

@@ -0,0 +1,605 @@
+/**
+ * Author:   subcrip
+ * Created:  2024-05-30 21:46:13
+ * Modified: 2024-05-30 22:30:38
+ * Elapsed:  44 minutes
+ */
+
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * This code should require C++14.
+ * However, it's only been tested with 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) remove_reference<decltype(container)>::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<>>;
+template <typename T> using oi = ostream_iterator<T>;
+template <typename T> using ii = istream_iterator<T>;
+
+/* 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 (auto& x : a) cin >> x;)
+#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
+#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#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> istream& operator>>(istream& in, pair<T, U>& p) {
+    return in >> p.first >> p.second;
+}
+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 */
+template <typename return_t>
+return_t qpow(ll b, ll p) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    return_t half = qpow<return_t>(b, p / 2);
+    if (p % 2 == 1) return half * half * b;
+    else return half * half;
+}
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+
+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; }
+};
+struct MLLd {
+    ll val, mdl;
+    MLLd(ll mdl, ll v = 0) : mdl(mdl), val(mod(v, mdl)) {}
+    MLLd(const MLLd& other) : mdl(other.mdl), val(other.val) {}
+    friend MLLd operator+(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val + rhs.val, lhs.mdl)); }
+    friend MLLd operator-(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - rhs.val, lhs.mdl)); }
+    friend MLLd operator*(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * rhs.val, lhs.mdl)); }
+    friend MLLd operator/(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * mod(inverse(rhs.val, lhs.mdl), lhs.mdl), lhs.mdl)); }
+    friend MLLd operator%(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - (lhs / rhs).val, lhs.mdl)); }
+    friend bool operator==(const MLLd& lhs, const MLLd& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLLd& lhs, const MLLd& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLLd& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLLd& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLLd& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLLd& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLLd& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+ostream& operator<<(ostream& out, const MLLd& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+istream& operator>>(istream& in, MLLd& 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)); });
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
+    vector<pair<T, U>> res;
+    auto a_it = a_first;
+    auto b_it = b_first;
+    for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
+        res.emplace_back(*a_it, *b_it);
+    }
+    return res;
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
+    vector<pair<T, U>> res;
+    if (n > 0) {
+        res.emplace_back(*a_first, *b_first);
+        for (size_t i = 1; i != n; ++i) {
+            res.emplace_back(*++a_first, *++b_first);
+        }
+    }
+    return res;
+}
+template <typename T>
+class ArithmeticIterator : bidirectional_iterator_tag {
+public:
+    using difference_type = ptrdiff_t;
+    using value_type = T;
+private:
+    value_type value;
+public:
+    ArithmeticIterator(const T& value) : value(value) {}
+    value_type operator*() const { return value; }
+    ArithmeticIterator<T>& operator++() { ++value; return *this; }
+    ArithmeticIterator<T>& operator--() { --value; return *this; }
+    bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
+};
+template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
+    return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
+}
+/////////////////////////////////////////////////////////
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+void solve() {
+    read(int, n, m);
+    vector<vector<pii>> edges(n + 1);
+    while (m--) {
+        read(int, w, u, v);
+        edgew(edges, u, v, w);
+    }
+    vector<int> sq;
+    vector<int> direction(n + 1, -1);
+    vector<int> ind(n + 1);
+    adj(ch, n);
+    int f = 1;
+    auto dfs = [&] (auto dfs, int v, int di) -> void {
+        if (direction[v] != -1) {
+            if (direction[v] != di) f = 0;
+            return;
+        }
+        direction[v] = di;
+        for (auto&& [u, type] : edges[v]) {
+            if (type == 1) {
+                // irrelevant
+                if (di == 1) {
+                    // right
+                    Edge(ch, u, v);
+                    ind[v] += 1;
+                } else {
+                    Edge(ch, v, u);
+                    ind[u] += 1;
+                }
+            } else {
+                // destined
+                if (di == 1) {
+                    Edge(ch, v, u);
+                    ind[u] += 1;
+                } else {
+                    Edge(ch, u, v);
+                    ind[v] += 1;
+                }
+            }
+            dfs(dfs, u, 1 ^ di);
+        }
+    };
+    for (int i = 1; i <= n ;++i) {
+        if (direction[i] == -1) {
+            dfs(dfs, i, 0);
+        }
+    }
+    if (f == 0) {
+        cout << "NO\n";
+        return;
+    }
+    deque<int> q;
+    for (int i = 1; i <= n; ++i) {
+        if (ind[i] == 0) {
+            q.emplace_back(i);
+        }
+    }
+    while (q.size()) {
+        int v = q.front(); q.pop_front();
+        sq.emplace_back(v);
+        for (auto&& u : ch[v]) {
+            if (--ind[u] == 0) {
+                q.emplace_back(u);
+            }
+        }
+    }
+    if (sq.size() != n) {
+        cout << "NO\n";
+        return;
+    }
+    vector<int> num(n + 1);
+    for (auto&& [i, x] : enumerate(sq)) {
+        num[x] = i;
+    }
+    cout << "YES\n";
+    for (int i = 1; i <= n; ++i) {
+        if (direction[i] == 1) {
+            // right
+            cout << "R ";
+        } else {
+            cout << "L ";
+        }
+        cout << num[i] << '\n';
+    }
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not 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 != (TOT_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1637e.cc

@@ -0,0 +1,583 @@
+/**
+ * Author:   subcrip
+ * Created:  2024-05-30 23:34:35
+ * Modified: 2024-05-30 23:56:21
+ * Elapsed:  21 minutes
+ */
+
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * This code should require C++14.
+ * However, it's only been tested with 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) remove_reference<decltype(container)>::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<>>;
+template <typename T> using oi = ostream_iterator<T>;
+template <typename T> using ii = istream_iterator<T>;
+
+/* 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 faster(um) __AS_PROCEDURE((um).reserve(1024); (um).max_load_factor(0.25);)
+#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 (auto& x : a) cin >> x;)
+#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
+#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#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> istream& operator>>(istream& in, pair<T, U>& p) {
+    return in >> p.first >> p.second;
+}
+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 */
+template <typename return_t>
+return_t qpow(ll b, ll p) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    return_t half = qpow<return_t>(b, p / 2);
+    if (p % 2 == 1) return half * half * b;
+    else return half * half;
+}
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+
+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; }
+};
+struct MLLd {
+    ll val, mdl;
+    MLLd(ll mdl, ll v = 0) : mdl(mdl), val(mod(v, mdl)) {}
+    MLLd(const MLLd& other) : mdl(other.mdl), val(other.val) {}
+    friend MLLd operator+(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val + rhs.val, lhs.mdl)); }
+    friend MLLd operator-(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - rhs.val, lhs.mdl)); }
+    friend MLLd operator*(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * rhs.val, lhs.mdl)); }
+    friend MLLd operator/(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * mod(inverse(rhs.val, lhs.mdl), lhs.mdl), lhs.mdl)); }
+    friend MLLd operator%(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - (lhs / rhs).val, lhs.mdl)); }
+    friend bool operator==(const MLLd& lhs, const MLLd& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLLd& lhs, const MLLd& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLLd& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLLd& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLLd& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLLd& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLLd& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+ostream& operator<<(ostream& out, const MLLd& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+istream& operator>>(istream& in, MLLd& 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)); });
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
+    vector<pair<T, U>> res;
+    auto a_it = a_first;
+    auto b_it = b_first;
+    for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
+        res.emplace_back(*a_it, *b_it);
+    }
+    return res;
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
+    vector<pair<T, U>> res;
+    if (n > 0) {
+        res.emplace_back(*a_first, *b_first);
+        for (size_t i = 1; i != n; ++i) {
+            res.emplace_back(*++a_first, *++b_first);
+        }
+    }
+    return res;
+}
+template <typename T>
+class ArithmeticIterator : bidirectional_iterator_tag {
+public:
+    using difference_type = ptrdiff_t;
+    using value_type = T;
+private:
+    value_type value;
+public:
+    ArithmeticIterator(const T& value) : value(value) {}
+    value_type operator*() const { return value; }
+    ArithmeticIterator<T>& operator++() { ++value; return *this; }
+    ArithmeticIterator<T>& operator--() { --value; return *this; }
+    bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
+};
+template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
+    return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+void solve() {
+    read(int, n, m);
+    readvec(int, a, n);
+    unordered_map<int, int, safe_hash> ct;
+    for (auto&& x : a) ct[x] += 1;
+    map<int, vector<ll>> cnt;
+    for (auto&& [x, t] : ct) cnt[t].emplace_back(x);
+    vector<pair<int, vector<ll>>> bk;
+    for (auto&& [t, v] : cnt) bk.emplace_back(t, v);
+    for (auto&& [t, v] : bk) {
+        sort(v.begin(), v.end(), greater());
+    }
+    int u = bk.size();
+    unordered_set<pii, pair_hash> ps;
+    for (int i = 0; i < m; ++i) {
+        read(int, x, y);
+        ps.emplace(minmax(x, y));
+    }
+    ll res = 0;
+    for (int i = 0; i < u; ++i) {
+        for (int j = 0; j < i; ++j) {
+            auto cmp = [&] (const pii& a, const pii& b) {
+                return bk[i].second[a.first] + bk[j].second[a.second] < bk[i].second[b.first] + bk[j].second[b.second];
+            };
+            unordered_set<pii, pair_hash> vis;
+            priority_queue<pii, vector<pii>, decltype(cmp)> pq(cmp);
+            pq.emplace(0, 0);
+            while (pq.size()) {
+                poptop(pq, u, v);
+                if (vis.count({u, v})) continue;
+                vis.emplace(u, v);
+                if (not ps.count(minmax(bk[i].second[u], bk[j].second[v]))) {
+                    res = max(res, (bk[i].first + bk[j].first) * (bk[i].second[u] + bk[j].second[v]));
+                    break;
+                }
+                if (u + 1 < bk[i].second.size()) pq.emplace(u + 1, v);
+                if (v + 1 < bk[j].second.size()) pq.emplace(u, v + 1);
+            }
+        }
+    }
+    // same
+    for (int i = 0; i < u; ++i) {
+        auto cmp = [&] (const pii& a, const pii& b) {
+            return bk[i].second[a.first] + bk[i].second[a.second] < bk[i].second[b.first] + bk[i].second[b.second];
+        };
+        unordered_set<pii, pair_hash> vis;
+        priority_queue<pii, vector<pii>, decltype(cmp)> pq(cmp);
+        pq.emplace(0, 0);
+        while (pq.size()) {
+            poptop(pq, u, v);
+            if (vis.count({u, v})) continue;
+            vis.emplace(u, v);
+            if (u != v and not ps.count(minmax(bk[i].second[u], bk[i].second[v]))) {
+                res = max(res, (bk[i].first + bk[i].first) * (bk[i].second[u] + bk[i].second[v]));
+                break;
+            }
+            if (u + 1 < bk[i].second.size()) pq.emplace(u + 1, v);
+            if (v + 1 < bk[i].second.size()) pq.emplace(u, v + 1);
+        }
+    }
+    cout << res << '\n';
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not 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 != (TOT_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1641c.cc

@@ -0,0 +1,704 @@
+/**
+ * Author:   subcrip
+ * Created:  2024-05-30 18:43:44
+ * Modified: 2024-05-30 20:44:48
+ * Elapsed:  121 minutes
+ */
+
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * This code should require C++14.
+ * However, it's only been tested with 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) remove_reference<decltype(container)>::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<>>;
+template <typename T> using oi = ostream_iterator<T>;
+template <typename T> using ii = istream_iterator<T>;
+
+/* 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 (auto& x : a) cin >> x;)
+#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
+#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#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> istream& operator>>(istream& in, pair<T, U>& p) {
+    return in >> p.first >> p.second;
+}
+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 */
+template <typename return_t>
+return_t qpow(ll b, ll p) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    return_t half = qpow<return_t>(b, p / 2);
+    if (p % 2 == 1) return half * half * b;
+    else return half * half;
+}
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+
+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; }
+};
+struct MLLd {
+    ll val, mdl;
+    MLLd(ll mdl, ll v = 0) : mdl(mdl), val(mod(v, mdl)) {}
+    MLLd(const MLLd& other) : mdl(other.mdl), val(other.val) {}
+    friend MLLd operator+(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val + rhs.val, lhs.mdl)); }
+    friend MLLd operator-(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - rhs.val, lhs.mdl)); }
+    friend MLLd operator*(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * rhs.val, lhs.mdl)); }
+    friend MLLd operator/(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * mod(inverse(rhs.val, lhs.mdl), lhs.mdl), lhs.mdl)); }
+    friend MLLd operator%(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - (lhs / rhs).val, lhs.mdl)); }
+    friend bool operator==(const MLLd& lhs, const MLLd& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLLd& lhs, const MLLd& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLLd& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLLd& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLLd& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLLd& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLLd& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+ostream& operator<<(ostream& out, const MLLd& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+istream& operator>>(istream& in, MLLd& 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)); });
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
+    vector<pair<T, U>> res;
+    auto a_it = a_first;
+    auto b_it = b_first;
+    for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
+        res.emplace_back(*a_it, *b_it);
+    }
+    return res;
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
+    vector<pair<T, U>> res;
+    if (n > 0) {
+        res.emplace_back(*a_first, *b_first);
+        for (size_t i = 1; i != n; ++i) {
+            res.emplace_back(*++a_first, *++b_first);
+        }
+    }
+    return res;
+}
+template <typename T>
+class ArithmeticIterator : bidirectional_iterator_tag {
+public:
+    using difference_type = ptrdiff_t;
+    using value_type = T;
+private:
+    value_type value;
+public:
+    ArithmeticIterator(const T& value) : value(value) {}
+    value_type operator*() const { return value; }
+    ArithmeticIterator<T>& operator++() { ++value; return *this; }
+    ArithmeticIterator<T>& operator--() { --value; return *this; }
+    bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
+};
+template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
+    return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
+}
+/////////////////////////////////////////////////////////
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+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);
+        pull(p);
+    }
+    
+    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 = INFLL;
+    void apply(const Tag& rhs) {
+        val = min(val, rhs.val);
+    }
+};
+struct Info {
+    ll val = -INFLL, loc = -1, inf_cnt = 0;
+    void apply(const Tag& rhs, size_t len) {
+        val = min(val, rhs.val);
+        // when the segment is not a leaf:
+        // set val according to the time of the operation removing all INFLL's
+        if (inf_cnt and rhs.val != INFLL) inf_cnt = 0, val = rhs.val;
+    }
+};
+Info operator+(const Info &a, const Info &b) {
+    // if the current Info is empty:
+    if (a.val == -INFLL) {
+        return b;
+    }
+    if (b.val == -INFLL) {
+        return a;
+    }
+    // merge two segments
+    if (not a.inf_cnt and not b.inf_cnt) {
+        return {
+            max(a.val, b.val),
+            a.loc,  // choose arbitrarily since no segment has INFLL
+            0,
+        };
+    } else if (a.inf_cnt) {
+        // the case of:
+        //   1. both segments have INFLL => { INFLL, [[invalid]], inf_cnt }
+        //   2. only the left one has
+        return {
+            // edge case: left segment only has one element
+            a.val == INFLL ? b.val : max(a.val, b.val),
+            a.loc,
+            a.inf_cnt + b.inf_cnt,
+        };
+    } else {
+        return {
+            // edge case: right segment only has one element
+            b.val == INFLL ? a.val : max(a.val, b.val),
+            b.loc,
+            a.inf_cnt + b.inf_cnt,
+        };
+    }
+}
+
+void solve() {
+    read(int, n, q);
+    segtree<Info, Tag> tr(n + 1);
+    for (int i = 1; i <= n; ++i) {
+        tr.set(i, {INFLL, i, 1});
+    }
+    vector<pii> queries;
+    vector<tiii> segments;  // "1" segments
+    for (int i = 0; i < q; ++i) {
+        read(int, op);
+        if (op == 0) {
+            read(int, l, r, x);
+            if (x == 0) {
+                tr.range_apply(l, r, {i});
+            } else {
+                segments.emplace_back(l, r, i);
+            }
+        } else {
+            read(int, j);
+            queries.emplace_back(j, i);
+        }
+    }
+    vector<int> one(n + 1, INF);  // when the status of point i is determined
+    for (auto&& [l, r, i] : segments) {
+        auto res = tr.range_query(l, r);
+        if (res.inf_cnt != 1) continue;
+        // edge case: l == r
+        if (l == r) one[res.loc] = min(one[res.loc], i);
+        // count in both the current "1" segment and all "0" segments.
+        else one[res.loc] = min(one[res.loc], max(i, int(res.val)));
+    }
+    for (auto&& [j, i] : queries) {
+        if (one[j] < i) {
+            cout << "YES\n";
+        } else if (tr.query(j).val < i) {
+            cout << "NO\n";
+        } else {
+            cout << "N/A\n";
+        }
+    }
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not 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 != (TOT_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1646e.cc

@@ -0,0 +1,543 @@
+/**
+ * Author:   subcrip
+ * Created:  2024-05-29 20:27:37
+ * Modified: 2024-05-30 10:28:54
+ * Elapsed:  841 minutes
+ */
+
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * This code should require C++14.
+ * However, it's only been tested with 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) remove_reference<decltype(container)>::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<>>;
+template <typename T> using oi = ostream_iterator<T>;
+template <typename T> using ii = istream_iterator<T>;
+
+/* 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 (auto& x : a) cin >> x;)
+#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
+#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#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> istream& operator>>(istream& in, pair<T, U>& p) {
+    return in >> p.first >> p.second;
+}
+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 */
+template <typename return_t>
+return_t qpow(ll b, ll p) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    return_t half = qpow<return_t>(b, p / 2);
+    if (p % 2 == 1) return half * half * b;
+    else return half * half;
+}
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+
+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; }
+};
+struct MLLd {
+    ll val, mdl;
+    MLLd(ll mdl, ll v = 0) : mdl(mdl), val(mod(v, mdl)) {}
+    MLLd(const MLLd& other) : mdl(other.mdl), val(other.val) {}
+    friend MLLd operator+(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val + rhs.val, lhs.mdl)); }
+    friend MLLd operator-(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - rhs.val, lhs.mdl)); }
+    friend MLLd operator*(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * rhs.val, lhs.mdl)); }
+    friend MLLd operator/(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * mod(inverse(rhs.val, lhs.mdl), lhs.mdl), lhs.mdl)); }
+    friend MLLd operator%(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - (lhs / rhs).val, lhs.mdl)); }
+    friend bool operator==(const MLLd& lhs, const MLLd& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLLd& lhs, const MLLd& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLLd& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLLd& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLLd& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLLd& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLLd& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+ostream& operator<<(ostream& out, const MLLd& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+istream& operator>>(istream& in, MLLd& 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)); });
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
+    vector<pair<T, U>> res;
+    auto a_it = a_first;
+    auto b_it = b_first;
+    for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
+        res.emplace_back(*a_it, *b_it);
+    }
+    return res;
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
+    vector<pair<T, U>> res;
+    if (n > 0) {
+        res.emplace_back(*a_first, *b_first);
+        for (size_t i = 1; i != n; ++i) {
+            res.emplace_back(*++a_first, *++b_first);
+        }
+    }
+    return res;
+}
+template <typename T>
+class ArithmeticIterator : bidirectional_iterator_tag {
+public:
+    using difference_type = ptrdiff_t;
+    using value_type = T;
+private:
+    value_type value;
+public:
+    ArithmeticIterator(const T& value) : value(value) {}
+    value_type operator*() const { return value; }
+    ArithmeticIterator<T>& operator++() { ++value; return *this; }
+    ArithmeticIterator<T>& operator--() { --value; return *this; }
+    bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
+};
+template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
+    return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
+}
+/////////////////////////////////////////////////////////
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+void solve() {
+    read(ll, n, m);
+    int t = lg2(n) + 1, N = m * t;
+    vector<bool> vis(N + 1);
+    vector<int> cnt(t + 1);
+    for (ll i = 2; i <= t; ++i) {
+        for (ll j = 1; j <= m; ++j) {
+            if (j * i > m and not vis[j * i]) cnt[i] += 1;
+            vis[j * i] = 1;
+        }
+    }
+    ll res = 0;
+    vector<bool> mark(n + 1);
+    for (ll i = 2; i <= n; ++i) {
+        if (mark[i]) continue;
+        for (ll j = 2, x = i * i; x <= n; ++j, x *= i) {
+            mark[x] = 1;
+            res += cnt[j];
+        }
+        res += m;
+    }
+    cout << res + 1 << '\n';
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not 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 != (TOT_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1650f.cc

@@ -0,0 +1,570 @@
+/**
+ * Author:   subcrip
+ * Created:  2024-05-29 17:05:56
+ * Modified: 2024-05-29 17:58:20
+ * Elapsed:  52 minutes
+ */
+
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * This code should require C++14.
+ * However, it's only been tested with 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) remove_reference<decltype(container)>::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<>>;
+template <typename T> using oi = ostream_iterator<T>;
+template <typename T> using ii = istream_iterator<T>;
+
+/* 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 (auto& x : a) cin >> x;)
+#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
+#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#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> istream& operator>>(istream& in, pair<T, U>& p) {
+    return in >> p.first >> p.second;
+}
+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 */
+template <typename return_t>
+return_t qpow(ll b, ll p) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    return_t half = qpow<return_t>(b, p / 2);
+    if (p % 2 == 1) return half * half * b;
+    else return half * half;
+}
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+
+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; }
+};
+struct MLLd {
+    ll val, mdl;
+    MLLd(ll mdl, ll v = 0) : mdl(mdl), val(mod(v, mdl)) {}
+    MLLd(const MLLd& other) : mdl(other.mdl), val(other.val) {}
+    friend MLLd operator+(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val + rhs.val, lhs.mdl)); }
+    friend MLLd operator-(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - rhs.val, lhs.mdl)); }
+    friend MLLd operator*(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * rhs.val, lhs.mdl)); }
+    friend MLLd operator/(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * mod(inverse(rhs.val, lhs.mdl), lhs.mdl), lhs.mdl)); }
+    friend MLLd operator%(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - (lhs / rhs).val, lhs.mdl)); }
+    friend bool operator==(const MLLd& lhs, const MLLd& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLLd& lhs, const MLLd& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLLd& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLLd& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLLd& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLLd& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLLd& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+ostream& operator<<(ostream& out, const MLLd& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+istream& operator>>(istream& in, MLLd& 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)); });
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
+    vector<pair<T, U>> res;
+    auto a_it = a_first;
+    auto b_it = b_first;
+    for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
+        res.emplace_back(*a_it, *b_it);
+    }
+    return res;
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
+    vector<pair<T, U>> res;
+    if (n > 0) {
+        res.emplace_back(*a_first, *b_first);
+        for (size_t i = 1; i != n; ++i) {
+            res.emplace_back(*++a_first, *++b_first);
+        }
+    }
+    return res;
+}
+template <typename T>
+class ArithmeticIterator : bidirectional_iterator_tag {
+public:
+    using difference_type = ptrdiff_t;
+    using value_type = T;
+private:
+    value_type value;
+public:
+    ArithmeticIterator(const T& value) : value(value) {}
+    value_type operator*() const { return value; }
+    ArithmeticIterator<T>& operator++() { ++value; return *this; }
+    ArithmeticIterator<T>& operator--() { --value; return *this; }
+    bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
+};
+template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
+    return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+void solve() {
+    read(int, n, m);
+    readvec(int, a, n);
+    vector<vector<tuple<ll, int, int>>> events(n);
+    for (int k = 1; k <= m; ++k) {
+        read(int, i, time, percent);
+        events[--i].emplace_back(time, percent, k);
+    }
+    ll start = 0;
+    vector<int> res;
+    for (int i = 0; i < n; ++i) {
+        int m = events[i].size();
+        vector<vector<pli>> dp(m + 1, vector<pli>(101));
+        for (int i = 0; i <= m; ++i) {
+            for (int j = 0; j <= 100; ++j) {
+                dp[i][j] = {INF, j};
+            }
+        }
+        dp[0][0] = {0, 0};
+        for (int j = 1; j <= m; ++j) {
+            auto [t, p, idx] = events[i][j - 1];
+            for (int k = 0; k <= 100; ++k) {
+                dp[j][k] = dp[j - 1][k];
+            }
+            for (int k = 0; k <= 100; ++k) {
+                int new_percent = min(100, dp[j - 1][k].second + p);
+                if (dp[j][new_percent].first > dp[j - 1][k].first + t) {
+                    dp[j][new_percent] = {dp[j - 1][k].first + t, dp[j - 1][k].second + p};
+                }
+            }
+        }
+        ll tm = dp[m][100].first;
+        if (tm + start > a[i]) {
+            cout << -1 << '\n';
+            return;
+        } else {
+            int k = dp[m][100].second;
+            for (int j = m; j >= 1; --j) {
+                auto [t, p, idx] = events[i][j - 1];
+                if (dp[j][min(100, k)] < dp[j - 1][min(100, k)]) {
+                    k -= p;
+                    res.emplace_back(idx);
+                }
+            }
+            start += tm;
+        }
+    }
+    cout << res.size() << '\n';
+    putvec(res);
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not 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 != (TOT_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1650g.cc

@@ -0,0 +1,582 @@
+/**
+ * Author:   subcrip
+ * Created:  2024-05-29 11:18:42
+ * Modified: 2024-05-29 12:02:15
+ * Elapsed:  43 minutes
+ */
+
+#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) remove_reference<decltype(container)>::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<>>;
+template <typename T> using oi = ostream_iterator<T>;
+template <typename T> using ii = istream_iterator<T>;
+
+/* 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 (auto& x : a) cin >> x;)
+#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
+#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#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> istream& operator>>(istream& in, pair<T, U>& p) {
+    return in >> p.first >> p.second;
+}
+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 */
+template <typename return_t>
+return_t qpow(ll b, ll p) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    return_t half = qpow<return_t>(b, p / 2);
+    if (p % 2 == 1) return half * half * b;
+    else return half * half;
+}
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+
+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; }
+};
+struct MLLd {
+    ll val, mdl;
+    MLLd(ll mdl, ll v = 0) : mdl(mdl), val(mod(v, mdl)) {}
+    MLLd(const MLLd& other) : mdl(other.mdl), val(other.val) {}
+    friend MLLd operator+(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val + rhs.val, lhs.mdl)); }
+    friend MLLd operator-(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - rhs.val, lhs.mdl)); }
+    friend MLLd operator*(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * rhs.val, lhs.mdl)); }
+    friend MLLd operator/(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * mod(inverse(rhs.val, lhs.mdl), lhs.mdl), lhs.mdl)); }
+    friend MLLd operator%(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - (lhs / rhs).val, lhs.mdl)); }
+    friend bool operator==(const MLLd& lhs, const MLLd& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLLd& lhs, const MLLd& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLLd& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLLd& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLLd& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLLd& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLLd& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+ostream& operator<<(ostream& out, const MLLd& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+istream& operator>>(istream& in, MLLd& 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)); });
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
+    vector<pair<T, U>> res;
+    auto a_it = a_first;
+    auto b_it = b_first;
+    for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
+        res.emplace_back(*a_it, *b_it);
+    }
+    return res;
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
+    vector<pair<T, U>> res;
+    if (n > 0) {
+        res.emplace_back(*a_first, *b_first);
+        for (size_t i = 1; i != n; ++i) {
+            res.emplace_back(*++a_first, *++b_first);
+        }
+    }
+    return res;
+}
+template <typename T>
+class ArithmeticIterator : bidirectional_iterator_tag {
+public:
+    using difference_type = ptrdiff_t;
+    using value_type = T;
+private:
+    value_type value;
+public:
+    ArithmeticIterator(const T& value) : value(value) {}
+    value_type operator*() const { return value; }
+    ArithmeticIterator<T>& operator++() { ++value; return *this; }
+    ArithmeticIterator<T>& operator--() { --value; return *this; }
+    bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
+};
+template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
+    return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+void solve() {
+    using mll = MLL<MDL>;
+    read(int, n, m);
+    read(int, s, t);
+    adj(ch, n);
+    vector<pii> edges;
+    while (m--) {
+        read(int, u, v);
+        edge(ch, u, v);
+        edges.emplace_back(u, v);
+    }
+    vector<int> dis(n + 1, INF);
+    vector<int> disrev(n + 1, INF);
+    vector<mll> cnt(n + 1), cntrev(n + 1);
+    vector<bool> vis(n + 1);
+    deque<pii> q;
+    q.emplace_back(0, s);
+    dis[s] = 0, cnt[s] = 1;
+    while (q.size()) {
+        popfront(q, d, v);
+        continue_or(vis[v], 1);
+        for (auto&& u : ch[v]) {
+            if (d + 1 < dis[u]) {
+                dis[u] = d + 1;
+                cnt[u] = cnt[v];
+                q.emplace_back(d + 1, u);
+            } else if (d + 1 == dis[u]) {
+                cnt[u] += cnt[v];
+            }
+        }
+    }
+    vis.assign(n + 1, 0);
+    q.clear();
+    q.emplace_back(0, t);
+    disrev[t] = 0, cntrev[t] = 1;
+    while (q.size()) {
+        popfront(q, d, v);
+        continue_or(vis[v], 1);
+        for (auto&& u : ch[v]) {
+            if (d + 1 < disrev[u]) {
+                disrev[u] = d + 1;
+                cntrev[u] = cntrev[v];
+                q.emplace_back(d + 1, u);
+            } else if (d + 1 == disrev[u]) {
+                cntrev[u] += cntrev[v];
+            }
+        }
+    }
+    mll res = 0;
+    for (auto&& [u, v] : edges) {
+        if (dis[u] == dis[v]) {
+            if (dis[v] + disrev[v] == dis[t]) {
+                res += cnt[u] * cntrev[v];
+            }
+            if (dis[u] + disrev[u] == dis[t]) {
+                res += cnt[v] * cntrev[u];
+            }
+        }
+    }
+    cout << res + cnt[t] << '\n';
+}
+
+int main() {
+#if __cplusplus < 201703L or defined(_MSC_VER) and not 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 != (TOT_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1654e.cc

@@ -0,0 +1,602 @@
+/**
+ * Author:   subcrip
+ * Created:  2024-05-28 23:03:59
+ * Modified: 2024-05-29 00:56:11
+ * Elapsed:  112 minutes
+ */
+
+#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) remove_reference<decltype(container)>::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<>>;
+template <typename T> using oi = ostream_iterator<T>;
+template <typename T> using ii = istream_iterator<T>;
+
+/* 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 (auto& x : a) cin >> x;)
+#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
+#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#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> istream& operator>>(istream& in, pair<T, U>& p) {
+    return in >> p.first >> p.second;
+}
+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 */
+template <typename return_t>
+return_t qpow(ll b, ll p) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    return_t half = qpow<return_t>(b, p / 2);
+    if (p % 2 == 1) return half * half * b;
+    else return half * half;
+}
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+
+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; }
+};
+struct MLLd {
+    ll val, mdl;
+    MLLd(ll mdl, ll v = 0) : mdl(mdl), val(mod(v, mdl)) {}
+    MLLd(const MLLd& other) : mdl(other.mdl), val(other.val) {}
+    friend MLLd operator+(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val + rhs.val, lhs.mdl)); }
+    friend MLLd operator-(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - rhs.val, lhs.mdl)); }
+    friend MLLd operator*(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * rhs.val, lhs.mdl)); }
+    friend MLLd operator/(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * mod(inverse(rhs.val, lhs.mdl), lhs.mdl), lhs.mdl)); }
+    friend MLLd operator%(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - (lhs / rhs).val, lhs.mdl)); }
+    friend bool operator==(const MLLd& lhs, const MLLd& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLLd& lhs, const MLLd& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLLd& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLLd& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLLd& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLLd& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLLd& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+ostream& operator<<(ostream& out, const MLLd& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+istream& operator>>(istream& in, MLLd& 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)); });
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
+    vector<pair<T, U>> res;
+    auto a_it = a_first;
+    auto b_it = b_first;
+    for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
+        res.emplace_back(*a_it, *b_it);
+    }
+    return res;
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
+    vector<pair<T, U>> res;
+    if (n > 0) {
+        res.emplace_back(*a_first, *b_first);
+        for (size_t i = 1; i != n; ++i) {
+            res.emplace_back(*++a_first, *++b_first);
+        }
+    }
+    return res;
+}
+template <typename T>
+class ArithmeticIterator : bidirectional_iterator_tag {
+public:
+    using difference_type = ptrdiff_t;
+    using value_type = T;
+private:
+    value_type value;
+public:
+    ArithmeticIterator(const T& value) : value(value) {}
+    value_type operator*() const { return value; }
+    ArithmeticIterator<T>& operator++() { ++value; return *this; }
+    ArithmeticIterator<T>& operator--() { --value; return *this; }
+    bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
+};
+template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
+    return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
+}
+/////////////////////////////////////////////////////////
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+template <typename Val, int LOG = 20>
+struct HashMapLL {
+  int N;
+  ll* keys;
+  Val* vals;
+  vector<int> IDS;
+  bitset<1 << LOG> used;
+  const int shift;
+  const uint64_t r = 11995408973635179863ULL;
+  HashMapLL()
+      : N(1 << LOG), keys(new ll[N]), vals(new Val[N]), shift(64 - __lg(N)) {}
+  int hash(ll x) {
+    static const uint64_t FIXED_RANDOM
+        = std::chrono::steady_clock::now().time_since_epoch().count();
+    return (uint64_t(x + FIXED_RANDOM) * r) >> shift;
+  }
+ 
+  int index(const ll& key) {
+    int i = 0;
+    for (i = hash(key); used[i] && keys[i] != key; (i += 1) &= (N - 1)) {}
+    return i;
+  }
+ 
+  Val& operator[](const ll& key) {
+    int i = index(key);
+    if (!used[i]) IDS.emplace_back(i), used[i] = 1, keys[i] = key, vals[i] = Val{};
+    return vals[i];
+  }
+  bool contain(const ll& key) {
+    int i = index(key);
+    return used[i] && keys[i] == key;
+  }
+ 
+  void reset(){
+    for(auto&& i : IDS) used[i] = 0;
+    IDS.clear();
+  }
+};
+
+HashMapLL<int> cnt, bk;
+HashMapLL<bool> has;
+
+int __solve(int n, const vector<int>& a) {
+    cnt.reset();
+    bk.reset();
+    // d <= sqrt(n)
+    constexpr int N = 1e5 + 10;
+    int sq = sqrt(N);
+    int res = 1;
+    for (int i = 0; i < n; ++i) {
+        for (ll k = 0; k <= sq; ++k) {
+            ll curr = a[i] - k * i;
+            cnt[imake(k, curr)] += 1;
+            res = max(res, cnt[imake(k, curr)]);
+        }
+    }
+    // d > sqrt(n)
+    for (int i = 0; i < n; ++i) {
+        has.reset();
+        for (int j = max(0, i - N / sq - 1); j < i; ++j) {
+            if ((a[i] - a[j]) % (i - j)) continue;
+            ll diff = (a[i] - a[j]) / (i - j);
+            ll start = a[i] - diff * i;
+            if (not has.contain(imake(diff, start))) {
+                bk[imake(diff, start)] += 1;
+                has[imake(diff, start)] = 1;
+                res = max(res, bk[imake(diff, start)] + 1);
+            }
+        }
+    }
+    return res;
+}
+
+void solve() {
+    read(int, n);
+    readvec(int, a, n);
+    int res1 = __solve(n, a);
+    reverse(a.begin(), a.end());
+    int res2 = __solve(n, a);
+    cout << n - max(res1, res2) << endl;
+}
+
+int main() {
+#if __cplusplus < 201703L or defined(_MSC_VER) and not 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 != (TOT_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
+}

src/bin/cf-1657e.cc

@@ -1,8 +1,8 @@
 /**
  * Author:   subcrip
  * Created:  2024-05-28 08:04:33
- * Modified: 2024-05-28 09:17:51
- * Elapsed:  73 minutes
+ * Modified: 2024-05-28 16:23:59
+ * Elapsed:  499 minutes
  */
 
 #pragma GCC optimize("Ofast")

src/bin/ctext_out.cc

@@ -1,16 +1,15 @@
 /**
  * Author:   subcrip
- * Created:  2024-05-28 08:04:33
- * Modified: 2024-05-28 09:17:51
- * Elapsed:  73 minutes
+ * Created:  2024-05-30 23:34:35
+ * Modified: 2024-05-30 23:56:21
+ * Elapsed:  21 minutes
  */
 
 #pragma GCC optimize("Ofast")
 /////////////////////////////////////////////////////////
 /**
- * Useful Macros
- *   by subcrip
- * (requires C++17)
+ * This code should require C++14.
+ * However, it's only been tested with C++17.
  */
 
 #include<bits/stdc++.h>
@@ -181,6 +180,7 @@ struct array_hash {
 };
 
 /* build data structures */
+#define faster(um) __AS_PROCEDURE((um).reserve(1024); (um).max_load_factor(0.25);)
 #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);)
@@ -270,6 +270,17 @@ std::ostream& operator<<(std::ostream& dest, const int128& value) {
 #define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
 
 /* math */
+template <typename return_t>
+return_t qpow(ll b, ll p) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    return_t half = qpow<return_t>(b, p / 2);
+    if (p % 2 == 1) return half * half * b;
+    else return half * half;
+}
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+
 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) {
@@ -471,7 +482,7 @@ template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container)
 }
 /////////////////////////////////////////////////////////
 
-#define SINGLE_TEST_CASE
+// #define SINGLE_TEST_CASE
 // #define DUMP_TEST_CASE 7219
 // #define TOT_TEST_CASE 10000
 
@@ -479,47 +490,74 @@ void dump() {}
 
 void dump_ignore() {}
 
-using mll = MLL<PRIME>;
-constexpr int N = 256;
-mll fact[N];
 void prep() {
-    fact[0] = 1;
-    for (int i = 1; i < N; ++i) {
-        fact[i] = fact[i - 1] * i;
-    }
 }
 
-template <typename return_t>
-return_t qpow(ll b, ll p) {
-    if (b == 0 and p != 0) return 0;
-    if (p == 0) return 1;
-    return_t half = qpow<return_t>(b, p / 2);
-    if (p % 2 == 1) return half * half * b;
-    else return half * half;
-}
-
-#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
-
 void solve() {
-    read(int, n, k);
-    vector<vector<mll>> dp(n, vector<mll>(k + 1));  // ps
-    for (int j = 0; j <= k; ++j) dp[0][j] = 1;
-    for (int i = 1; i < n; ++i) {
-        vector<mll> ndp(k + 1);
-        for (int j = 1; j <= k; ++j) {
-            for (int l = 1; l <= i; ++l) {
-                ndp[j] += comb(i, l) * dp[i - l][j - 1] * qpow<mll>(k - j + 1, ll(1) * (i - l) * l + ll(1) * l * (l - 1) / 2);
+    read(int, n, m);
+    readvec(int, a, n);
+    unordered_map<int, int, safe_hash> ct;
+    for (auto&& x : a) ct[x] += 1;
+    map<int, vector<ll>> cnt;
+    for (auto&& [x, t] : ct) cnt[t].emplace_back(x);
+    vector<pair<int, vector<ll>>> bk;
+    for (auto&& [t, v] : cnt) bk.emplace_back(t, v);
+    for (auto&& [t, v] : bk) {
+        sort(v.begin(), v.end(), greater());
+    }
+    int u = bk.size();
+    unordered_set<pii, pair_hash> ps;
+    for (int i = 0; i < m; ++i) {
+        read(int, x, y);
+        ps.emplace(minmax(x, y));
+    }
+    ll res = 0;
+    for (int i = 0; i < u; ++i) {
+        for (int j = 0; j < i; ++j) {
+            auto cmp = [&] (const pii& a, const pii& b) {
+                return bk[i].second[a.first] + bk[j].second[a.second] < bk[i].second[b.first] + bk[j].second[b.second];
+            };
+            unordered_set<pii, pair_hash> vis;
+            priority_queue<pii, vector<pii>, decltype(cmp)> pq(cmp);
+            pq.emplace(0, 0);
+            while (pq.size()) {
+                poptop(pq, u, v);
+                if (vis.count({u, v})) continue;
+                vis.emplace(u, v);
+                if (not ps.count(minmax(bk[i].second[u], bk[j].second[v]))) {
+                    res = max(res, (bk[i].first + bk[j].first) * (bk[i].second[u] + bk[j].second[v]));
+                    break;
+                }
+                if (u + 1 < bk[i].second.size()) pq.emplace(u + 1, v);
+                if (v + 1 < bk[j].second.size()) pq.emplace(u, v + 1);
             }
         }
-        for (int j = 1; j <= k; ++j) {
-            dp[i][j] = dp[i][j - 1] + ndp[j];
+    }
+    // same
+    for (int i = 0; i < u; ++i) {
+        auto cmp = [&] (const pii& a, const pii& b) {
+            return bk[i].second[a.first] + bk[i].second[a.second] < bk[i].second[b.first] + bk[i].second[b.second];
+        };
+        unordered_set<pii, pair_hash> vis;
+        priority_queue<pii, vector<pii>, decltype(cmp)> pq(cmp);
+        pq.emplace(0, 0);
+        while (pq.size()) {
+            poptop(pq, u, v);
+            if (vis.count({u, v})) continue;
+            vis.emplace(u, v);
+            if (u != v and not ps.count(minmax(bk[i].second[u], bk[i].second[v]))) {
+                res = max(res, (bk[i].first + bk[i].first) * (bk[i].second[u] + bk[i].second[v]));
+                break;
+            }
+            if (u + 1 < bk[i].second.size()) pq.emplace(u + 1, v);
+            if (v + 1 < bk[i].second.size()) pq.emplace(u, v + 1);
         }
     }
-    cout << dp[n - 1][k] << '\n';
+    cout << res << '\n';
 }
 
 int main() {
-#if __cplusplus < 201703L or defined(_MSC_VER) and not defined(__clang__)
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
     assert(false && "incompatible compiler variant detected.");
 #endif
     untie, cout.tie(NULL);

src/bin/saikr-1540.cc

@@ -0,0 +1,109 @@
+/**
+ * Author:   subcrip
+ * Created:  2024-05-29 13:43:45
+ * Modified: 2024-05-29 14:11:38
+ * Elapsed:  27 minutes
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+struct quick_union {
+    vector<size_t> c, sz;
+    int n;
+    quick_union(size_t n) : n(n), c(n), sz(n) {
+        clear();
+    }
+
+    void clear() {
+        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)];
+    }
+};
+
+int main() {
+    int n, m; cin >> n >> m;
+    vector<vector<int>> a(n, vector<int>(m));
+    for (int i = 0; i < n; ++i) {
+        for (int j = 0; j < m; ++j) {
+            cin >> a[i][j];
+        }
+    }
+    int res = 0;
+    auto dfs = [&] (auto dfs, const vector<vector<int>>& a, int acc) -> void {
+        quick_union qu(n * m);
+        unordered_set<int> has;
+        auto construct = [&] (int id) -> vector<vector<int>> {
+            vector<vector<int>> ret = a;
+            for (int i = 0; i < n; ++i) {
+                for (int j = 0; j < m; ++j) {
+                    if (qu.query(i * m + j) == id) {
+                        ret[i][j] = 0;
+                    }
+                }
+            }
+            for (int j = 0; j < m; ++j) {
+                int ptr = n - 1;
+                for (int i = n - 1; i >= 0; --i) {
+                    while (ptr >= 0 and ret[ptr][j] == 0) {
+                        --ptr;
+                    }
+                    if (ptr < 0) ret[i][j] = 0;
+                    else ret[i][j] = ret[ptr--][j];
+                }
+            }
+            return ret;
+        };
+        for (int i = 0; i < n; ++i) {
+            for (int j = 0; j < m; ++j) {
+                if (a[i][j] == 0) continue;
+                if (i - 1 >= 0 and a[i][j] == a[i - 1][j]) {
+                    qu.merge(i * m + j, (i - 1) * m + j);
+                }
+                if (i + 1 < n and a[i][j] == a[i + 1][j]) {
+                    qu.merge(i * m + j, (i + 1) * m + j);
+                }
+                if (j - 1 >= 0 and a[i][j] == a[i][j - 1]) {
+                    qu.merge(i * m + j, i * m + j - 1);
+                }
+                if (j + 1 < n and a[i][j] == a[i][j + 1]) {
+                    qu.merge(i * m + j, i * m + j + 1);
+                }
+            }
+        }
+        int f = 0;
+        for (int i = 0; i < n; ++i) {
+            for (int j = 0; j < m; ++j) {
+                if (a[i][j] == 0 or has.count(qu.query(i * m + j))) continue;
+                if (qu.query_size(i * m + j) >= 3) {
+                    f = 1;
+                    dfs(dfs, construct(qu.query(i * m + j)), acc + qu.query_size(i * m + j));
+                }
+                has.emplace(qu.query(i * m + j));
+            }
+        }
+        if (not f) {
+            res = max(res, acc);
+        }
+    };
+    dfs(dfs, a, 0);
+    cout << res << '\n';
+}
+

src/bin/saikr-1541.cc

@@ -0,0 +1,54 @@
+/**
+ * Author:   subcrip
+ * Created:  2024-05-29 14:25:39
+ * Modified: 2024-05-29 19:44:59
+ * Elapsed:  319 minutes
+ */
+
+#pragma GCC optimize("Ofast")
+#include <bits/stdc++.h>
+using namespace std;
+
+using ll = long long ;
+
+pair<vector<int>, vector<int>> factcount(int n) {
+    vector<bool> not_prime(n + 1);
+    vector<int> res(n + 1), num(n + 1);
+    vector<int> primes;
+    res[1] = 1;
+    for (int i = 2; i <= n; ++i) {
+        if (not not_prime[i]) {
+            res[i] = 2;
+            num[i] = 1;
+            primes.emplace_back(i);
+        }
+        for (auto&& x : primes) {
+            if (i * x > n) break;
+            not_prime[i * x] = 1;
+            if (i % x == 0) {
+                num[i * x] = num[i] + 1;
+                res[i * x] = res[i] / num[i * x] * (num[i * x] + 1);
+                break;
+            }
+            num[i * x] = 1;
+            res[i * x] = res[i] * 2;
+        }
+    }
+    return {primes, res};
+}
+
+int main() {
+    int n; cin >> n;
+    auto [primes, cnt] = factcount(n);
+    ll res = 0;
+    for (auto&& x : primes) {
+        int ab = n - x;
+        if (ab <= 0 or ab > n) continue;
+        if (ab == 1) {
+            res += 1;
+        } else if (cnt[ab] > 2) {
+            res += cnt[ab];
+        }
+    }
+    cout << res << '\n';
+}

src/bin/std.in

@@ -1,2 +1,13 @@
-42 13
+3
+6 1
+6 3 6 7 3 3
+3 6
+2 0
+3 4
+7 4
+1 2 2 3 1 5 1
+1 5
+3 5
+1 3
+2 5
 

src/bin/template.cc

@@ -1,9 +1,8 @@
 #pragma GCC optimize("Ofast")
 /////////////////////////////////////////////////////////
 /**
- * Useful Macros
- *   by subcrip
- * (requires C++17)
+ * This code should require C++14.
+ * However, it's only been tested with C++17.
  */
 
 #include<bits/stdc++.h>
@@ -174,6 +173,7 @@ struct array_hash {
 };
 
 /* build data structures */
+#define faster(um) __AS_PROCEDURE((um).reserve(1024); (um).max_load_factor(0.25);)
 #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);)
@@ -490,7 +490,7 @@ void solve() {
 }
 
 int main() {
-#if __cplusplus < 201703L or defined(_MSC_VER) and not defined(__clang__)
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
     assert(false && "incompatible compiler variant detected.");
 #endif
     untie, cout.tie(NULL);

src/bin/test.cc

@@ -1,13 +1,546 @@
 /**
  * Author:   subcrip
- * Created:  0000-05-26 01:17:23
- * Modified: 2024-05-26 01:18:31
- * Elapsed:  1064521446 minutes
+ * Created:  2024-05-29 19:36:48
+ * Modified: 2024-05-29 19:41:14
+ * Elapsed:  4 minutes
  */
 
-#include <bits/stdc++.h>
+#pragma GCC optimize("Ofast")
+/////////////////////////////////////////////////////////
+/**
+ * This code should require C++14.
+ * However, it's only been tested with C++17.
+ */
+
+#include<bits/stdc++.h>
 using namespace std;
 
-int main() {
-    do {} while (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) remove_reference<decltype(container)>::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<>>;
+template <typename T> using oi = ostream_iterator<T>;
+template <typename T> using ii = istream_iterator<T>;
+
+/* 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 (auto& x : a) cin >> x;)
+#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
+#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
+#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
+#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> istream& operator>>(istream& in, pair<T, U>& p) {
+    return in >> p.first >> p.second;
+}
+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 */
+template <typename return_t>
+return_t qpow(ll b, ll p) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    return_t half = qpow<return_t>(b, p / 2);
+    if (p % 2 == 1) return half * half * b;
+    else return half * half;
+}
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+
+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; }
+};
+struct MLLd {
+    ll val, mdl;
+    MLLd(ll mdl, ll v = 0) : mdl(mdl), val(mod(v, mdl)) {}
+    MLLd(const MLLd& other) : mdl(other.mdl), val(other.val) {}
+    friend MLLd operator+(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val + rhs.val, lhs.mdl)); }
+    friend MLLd operator-(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - rhs.val, lhs.mdl)); }
+    friend MLLd operator*(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * rhs.val, lhs.mdl)); }
+    friend MLLd operator/(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val * mod(inverse(rhs.val, lhs.mdl), lhs.mdl), lhs.mdl)); }
+    friend MLLd operator%(const MLLd& lhs, const MLLd& rhs) { return MLLd(lhs.mdl, mod(lhs.val - (lhs / rhs).val, lhs.mdl)); }
+    friend bool operator==(const MLLd& lhs, const MLLd& rhs) { return lhs.val == rhs.val; }
+    friend bool operator!=(const MLLd& lhs, const MLLd& rhs) { return lhs.val != rhs.val; }
+    void operator+=(const MLLd& rhs) { val = (*this + rhs).val; }
+    void operator-=(const MLLd& rhs) { val = (*this - rhs).val; }
+    void operator*=(const MLLd& rhs) { val = (*this * rhs).val; }
+    void operator/=(const MLLd& rhs) { val = (*this / rhs).val; }
+    void operator%=(const MLLd& rhs) { val = (*this % rhs).val; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+ostream& operator<<(ostream& out, const MLLd& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+istream& operator>>(istream& in, MLLd& 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)); });
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
+    vector<pair<T, U>> res;
+    auto a_it = a_first;
+    auto b_it = b_first;
+    for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
+        res.emplace_back(*a_it, *b_it);
+    }
+    return res;
+}
+template <typename T, typename U, typename Iterator_T, typename Iterator_U>
+vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
+    vector<pair<T, U>> res;
+    if (n > 0) {
+        res.emplace_back(*a_first, *b_first);
+        for (size_t i = 1; i != n; ++i) {
+            res.emplace_back(*++a_first, *++b_first);
+        }
+    }
+    return res;
+}
+template <typename T>
+class ArithmeticIterator : bidirectional_iterator_tag {
+public:
+    using difference_type = ptrdiff_t;
+    using value_type = T;
+private:
+    value_type value;
+public:
+    ArithmeticIterator(const T& value) : value(value) {}
+    value_type operator*() const { return value; }
+    ArithmeticIterator<T>& operator++() { ++value; return *this; }
+    ArithmeticIterator<T>& operator--() { --value; return *this; }
+    bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
+};
+template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
+    return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
+}
+/////////////////////////////////////////////////////////
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+vector<int> factcount(int n) {
+    vector<bool> not_prime(n + 1);
+    vector<int> res(n + 1), num(n + 1);
+    res[1] = 1;
+    for (int i = 2; i <= n; ++i) {
+        if (not not_prime[i]) {
+            res[i] = 2;
+            num[i] = 1;
+        }
+        for (auto&& x : res) {
+            if (i * x > n) break;
+            not_prime[i * x] = 1;
+            if (i % x == 0) {
+                num[i * x] = num[i] + 1;
+                res[i * x] = res[i] / num[i * x] * (num[i * x] + 1);
+                break;
+            }
+            num[i * x] = 1;
+            res[i * x] = res[i] * 2;
+        }
+    }
+    return res;
+}
+
+void solve() {
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not 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 != (TOT_TEST_CASE)) {
+            solve();
+        } else if (i + 1 == (DUMP_TEST_CASE)) {
+            dump();
+        } else {
+            dump_ignore();
+        }
+#else
+        solve();
+#endif
+    }
+#endif
 }

src/bin/test.py

@@ -4,17 +4,12 @@ from os import system
 import io
 
 if __name__ == '__main__':
-    while True:
-        n = randint(1, 5)
-        data = io.StringIO()
-        print(1, file=data)
-        print(n, file=data)
-        for i in range(n - 1):
-            print(f'{i + 1} {randint(i + 2, n)}', file=data)
-        with open('std.in', 'w') as f:
-            f.write(data.getvalue())
-        system('./a.out < std.in > std.out')
-        with open('std.out') as f:
-            ans = f.read().strip().split(' ')
-            if '0' in ans:
-                break
+    n = 8
+    m = 8
+    st = set()
+    for i in range(1, n + 1):
+        for j in range(1, m + 1):
+            print(i ** j, end='\t')
+            st.add(i ** j)
+        print()
+    print(len(st))