diff --git a/src/bin/a.cc b/src/bin/a.cc
index 77478fb..a3dc34e 100644
--- a/src/bin/a.cc
+++ b/src/bin/a.cc
@@ -25,7 +25,7 @@ using ull = unsigned long long;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
-using ld = long double;
+using ld = __float128;  // up to 1e-9 precision in binary search
 using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
 using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
 using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
@@ -48,6 +48,7 @@ constexpr int INF = 0x3f3f3f3f;
 constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
 constexpr ll MDL = 1e9 + 7;
 constexpr ll PRIME = 998'244'353;
+constexpr ll PRIMELL = 901017227882342239LL;
 constexpr ll MDL1 = 8784491;
 constexpr ll MDL2 = PRIME;
 constexpr int128 INT128_MAX = numeric_limits<int128>::max();
@@ -96,9 +97,9 @@ struct igt {
 
 /* 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;)
+#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 {
@@ -132,13 +133,15 @@ struct pair_hash {
 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 {
+    safe_hash hasher;
     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;
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * pw2) % __array_hash_mdl2;
             pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
             pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
         }
@@ -173,7 +176,7 @@ template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, s
 /* io */
 #define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
 
-// add declarations to avoid cyclic dependency
+// add declarations to avoid circular dependency
 template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
 template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
 template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
@@ -239,14 +242,14 @@ std::ostream& operator<<(std::ostream& dest, const int128& value) {
 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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
-#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : a) cin >> x;)
-#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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 readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
 #define deb(...) debug(make_tuple(__VA_ARGS__))
 
 /* pops */
@@ -293,7 +296,7 @@ ll qpow(ll b, ll p, ll mod) {
 #pragma GCC diagnostic ignored "-Wparentheses"
 // Accurately find `i` 'th root of `n` (taking the floor)
 inline ll root(ll n, ll i) {
-    ll l = 0, r = pow(LLONG_MAX, ld(1) / i);
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
     while (l < r) {
         ll mid = l + r + 1 >> 1;
         if (qpow<int128>(mid, i) <= n) {
@@ -393,7 +396,7 @@ vector<int> calc_z(string t) {  // z function of t
     }
     return z;
 }
-vector<int> kmp(string s, string t) {  // find all t in s
+vector<int> kmp(const string& s, const string& t) {  // find all t in s
     string cur = t + '#' + s;
     int sz1 = s.size(), sz2 = t.size();
     vector<int> v;
@@ -403,7 +406,7 @@ vector<int> kmp(string s, string t) {  // find all t in s
     }
     return v;
 }
-int period(string s) {  // find the length of shortest recurring period
+int period(const 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) {
@@ -421,8 +424,8 @@ template <ll mdl> struct MLL {
     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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
@@ -537,26 +540,13 @@ void prep() {
 
 // __attribute__((target("popcnt")))
 void solve() {
-    read(int, n, k);
-    readvec(int, a, n);
-    for (int i = 0; i < n; ++i) {
-        int has = 0;
-        for (int j = 0; j < n; ++j) {
-            if (i == j) continue;
-            has |= abs(a[i] - a[j]) % k == 0;
-        }
-        if (has == 0) {
-            cout << "YES\n";
-            cout << i + 1 << '\n';
-            return;
-        }
-    }
-    cout << "NO\n";
+    read(int, x, y, z);
+    cout << min({x / 2, y, z}) << '\n';
 }
 
 int main() {
 #if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
-    assert(false && "incompatible compiler variant detected.");
+    static_assert(false, "incompatible compiler variant detected.");
 #endif
     untie;
     prep();
diff --git a/src/bin/b.cc b/src/bin/b.cc
index 21a6553..070288a 100644
--- a/src/bin/b.cc
+++ b/src/bin/b.cc
@@ -25,7 +25,7 @@ using ull = unsigned long long;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
-using ld = long double;
+using ld = __float128;  // up to 1e-9 precision in binary search
 using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
 using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
 using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
@@ -48,6 +48,7 @@ constexpr int INF = 0x3f3f3f3f;
 constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
 constexpr ll MDL = 1e9 + 7;
 constexpr ll PRIME = 998'244'353;
+constexpr ll PRIMELL = 901017227882342239LL;
 constexpr ll MDL1 = 8784491;
 constexpr ll MDL2 = PRIME;
 constexpr int128 INT128_MAX = numeric_limits<int128>::max();
@@ -96,9 +97,9 @@ struct igt {
 
 /* 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;)
+#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 {
@@ -132,13 +133,15 @@ struct pair_hash {
 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 {
+    safe_hash hasher;
     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;
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * pw2) % __array_hash_mdl2;
             pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
             pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
         }
@@ -173,7 +176,7 @@ template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, s
 /* io */
 #define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
 
-// add declarations to avoid cyclic dependency
+// add declarations to avoid circular dependency
 template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
 template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
 template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
@@ -239,14 +242,14 @@ std::ostream& operator<<(std::ostream& dest, const int128& value) {
 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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
-#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : a) cin >> x;)
-#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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 readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
 #define deb(...) debug(make_tuple(__VA_ARGS__))
 
 /* pops */
@@ -293,7 +296,7 @@ ll qpow(ll b, ll p, ll mod) {
 #pragma GCC diagnostic ignored "-Wparentheses"
 // Accurately find `i` 'th root of `n` (taking the floor)
 inline ll root(ll n, ll i) {
-    ll l = 0, r = pow(LLONG_MAX, ld(1) / i);
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
     while (l < r) {
         ll mid = l + r + 1 >> 1;
         if (qpow<int128>(mid, i) <= n) {
@@ -393,7 +396,7 @@ vector<int> calc_z(string t) {  // z function of t
     }
     return z;
 }
-vector<int> kmp(string s, string t) {  // find all t in s
+vector<int> kmp(const string& s, const string& t) {  // find all t in s
     string cur = t + '#' + s;
     int sz1 = s.size(), sz2 = t.size();
     vector<int> v;
@@ -403,7 +406,7 @@ vector<int> kmp(string s, string t) {  // find all t in s
     }
     return v;
 }
-int period(string s) {  // find the length of shortest recurring period
+int period(const 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) {
@@ -421,8 +424,8 @@ template <ll mdl> struct MLL {
     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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
@@ -538,18 +541,17 @@ void prep() {
 // __attribute__((target("popcnt")))
 void solve() {
     read(int, n);
-    int res = 1;
-    int curr = 1;
-    while (curr < n) {
-        res += 1;
-        curr += curr + 2;
+    read(string, a);
+    if (a[0] == '1' or a[n - 1] == '1') {
+        cout << "Alice\n";
+    } else {
+        cout << "Bob\n";
     }
-    cout << res << '\n';
 }
 
 int main() {
 #if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
-    assert(false && "incompatible compiler variant detected.");
+    static_assert(false, "incompatible compiler variant detected.");
 #endif
     untie;
     prep();
diff --git a/src/bin/c.cc b/src/bin/c.cc
index eec5749..592ecd7 100644
--- a/src/bin/c.cc
+++ b/src/bin/c.cc
@@ -25,7 +25,7 @@ using ull = unsigned long long;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
-using ld = long double;
+using ld = __float128;  // up to 1e-9 precision in binary search
 using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
 using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
 using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
@@ -48,6 +48,7 @@ constexpr int INF = 0x3f3f3f3f;
 constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
 constexpr ll MDL = 1e9 + 7;
 constexpr ll PRIME = 998'244'353;
+constexpr ll PRIMELL = 901017227882342239LL;
 constexpr ll MDL1 = 8784491;
 constexpr ll MDL2 = PRIME;
 constexpr int128 INT128_MAX = numeric_limits<int128>::max();
@@ -96,9 +97,9 @@ struct igt {
 
 /* 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;)
+#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 {
@@ -132,13 +133,15 @@ struct pair_hash {
 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 {
+    safe_hash hasher;
     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;
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * pw2) % __array_hash_mdl2;
             pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
             pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
         }
@@ -173,7 +176,7 @@ template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, s
 /* io */
 #define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
 
-// add declarations to avoid cyclic dependency
+// add declarations to avoid circular dependency
 template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
 template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
 template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
@@ -239,14 +242,14 @@ std::ostream& operator<<(std::ostream& dest, const int128& value) {
 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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
-#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : a) cin >> x;)
-#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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 readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
 #define deb(...) debug(make_tuple(__VA_ARGS__))
 
 /* pops */
@@ -293,7 +296,7 @@ ll qpow(ll b, ll p, ll mod) {
 #pragma GCC diagnostic ignored "-Wparentheses"
 // Accurately find `i` 'th root of `n` (taking the floor)
 inline ll root(ll n, ll i) {
-    ll l = 0, r = pow(LLONG_MAX, ld(1) / i);
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
     while (l < r) {
         ll mid = l + r + 1 >> 1;
         if (qpow<int128>(mid, i) <= n) {
@@ -393,7 +396,7 @@ vector<int> calc_z(string t) {  // z function of t
     }
     return z;
 }
-vector<int> kmp(string s, string t) {  // find all t in s
+vector<int> kmp(const string& s, const string& t) {  // find all t in s
     string cur = t + '#' + s;
     int sz1 = s.size(), sz2 = t.size();
     vector<int> v;
@@ -403,7 +406,7 @@ vector<int> kmp(string s, string t) {  // find all t in s
     }
     return v;
 }
-int period(string s) {  // find the length of shortest recurring period
+int period(const 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) {
@@ -421,8 +424,8 @@ template <ll mdl> struct MLL {
     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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
@@ -524,7 +527,7 @@ constexpr std::array<T, N> __initarray(const T& value) {
 }
 /*******************************************************/
 
-// #define SINGLE_TEST_CASE
+#define SINGLE_TEST_CASE
 // #define DUMP_TEST_CASE 7219
 // #define TOT_TEST_CASE 10000
 
@@ -535,42 +538,92 @@ void dump_ignore() {}
 void prep() {
 }
 
-// __attribute__((target("popcnt")))
-void solve() {
-    read(int, n);
-    read(ll, k);
-    k -= 1;
-    vector<int> res(n);
-    int l = 0, r = n - 1;
-    for (int i = n - 2; ~i; --i) {
-        int bit;
-        if (i > 63) {
-            bit = 0;
-        } else {
-            bit = k >> i & 1;
-            k ^= ll(bit) << i;
-        }
-        if (bit == 0) {
-            res[l++] = n - 1 - i;
-        } else {
-            res[r--] = n - 1 - i;
+template<typename T>
+struct BIT {
+    int n;
+    vector<T> c;
+    BIT(size_t n) : n(n), c(n + 1) {}
+    void add(size_t i, const T& k) {
+        while (i <= n) {
+            c[i] += k;
+            i += lowbit(i);
         }
     }
-    if (k) {
-        cout << -1 << '\n';
-    } else {
-        assert(l == r);
-        res[l] = n;
-        for (auto&& x : res) {
-            cout << x << ' ';
+    T getsum(size_t i) {
+        T res = {};
+        while (i) {
+            res += c[i];
+            i -= lowbit(i);
+        }
+        return res;
+    }
+};
+
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, n, m);
+    n += 1;
+    vector cntrj(n, vector<int>(26));
+    vector ac(n, vector<bool>(26));
+    vector<pil> status(n);
+
+    vector<tuple<string, int, ll, int>> events;
+    vector<ll> oc = { ll(26) << 32 };
+    for (int i = 0; i < m; ++i) {
+        ll time = 0;
+        read(string, raw_time);
+        time += stoi(raw_time.substr(0, 2)) * 60 + stoi(raw_time.substr(3, 2));
+        read(int, team);
+        read(char, raw_no);
+        int no = raw_no - 'A';
+        read(string, raw_stat);
+        int stat = raw_stat == "AC";
+        bool upd = team == 0 and stat and not ac[team][no];
+        if (stat) {
+            if (ac[team][no]) {
+                ;;
+            } else {
+                ac[team][no] = 1;
+                status[team].first += 1;
+                status[team].second += time + ll(1) * 20 * cntrj[team][no];
+            }
+        } else {
+            cntrj[team][no] += 1;
+        }
+        // deb(team, status[team]);
+        ll currstatus = (26 - ll(1) * status[team].first) << 32 bitor status[team].second;
+        oc.emplace_back(currstatus);
+        events.emplace_back(raw_time, team, currstatus, upd ? no : -1);
+    }
+
+    sort(oc.begin(), oc.end());
+    int t = unique(oc.begin(), oc.end()) - oc.begin();
+    oc.resize(t);
+    auto get = [&] (ll x) { return lower_bound(oc.begin(), oc.end(), x) - oc.begin(); };
+
+    BIT<int> tr(t);
+
+    vector<ll> curr(n, (ll(1) * 26) << 32);
+    tr.add((ll(1) * 26) << 32, n);
+
+    for (auto&& [raw_time, team, penalty, no] : events) {
+        int old;
+        if (no != -1) {
+            old = tr.getsum(get(curr[0])) + 1;
+        }
+        tr.add(get(curr[team]) + 1, -1);
+        curr[team] = penalty;
+        tr.add(get(curr[team]) + 1, 1);
+        if (no != -1) {
+            cout << raw_time << ' ' << char(no + 'A') << " #" << old << " -> #" << tr.getsum(get(curr[0])) + 1 << '\n';
         }
-        cout << '\n';
     }
 }
 
 int main() {
 #if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
-    assert(false && "incompatible compiler variant detected.");
+    static_assert(false, "incompatible compiler variant detected.");
 #endif
     untie;
     prep();
diff --git a/src/bin/cf-815c.cc b/src/bin/cf-815c.cc
new file mode 100644
index 0000000..e553711
--- /dev/null
+++ b/src/bin/cf-815c.cc
@@ -0,0 +1,632 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+constexpr int N = 5010;
+ll dp[N][N][2];
+
+// __attribute__((target("popcnt")))
+void solve() {
+    memset(dp, 0x3f, sizeof(dp));
+
+    read(int, n, tot);
+    vector<int> a(n + 1), b(n + 1);
+    adj(ch, n);
+
+    for (int i = 1; i <= n; ++i) {
+        read(int, c, d);
+        a[i] = c, b[i] = c - d;
+        if (i >= 2) {
+            read(int, j);
+            edge(ch, i, j);
+        }
+    }
+
+    vector<int> sz(n + 1);
+    {
+        auto dfs = [&] (auto dfs, int v, int pa) -> void {
+            sz[v] = 1;
+            for (auto&& u : ch[v]) {
+                if (u == pa) continue;
+                dfs(dfs, u, v);
+                sz[v] += sz[u];
+            }
+        };
+        dfs(dfs, 1, 0);
+    }
+
+    // vector dp(n + 1, vector(n + 1, vector<ll>(2, INFLL)));
+    {
+        auto dfs = [&] (auto dfs, int v, int pa) -> void {
+            for (auto&& u : ch[v]) {
+                if (u == pa) continue;
+                dfs(dfs, u, v);
+            }
+            int curr = 1;
+            dp[v][0][0] = 0;
+            dp[v][1][0] = a[v];
+            dp[v][1][1] = b[v];
+            for (auto&& u : ch[v]) {
+                if (u == pa) continue;
+                for (int j = curr; ~j; --j) {
+                    for (int k = 0; k <= sz[u]; ++k) {
+                        chmin(dp[v][j + k][0], dp[u][k][0] + dp[v][j][0]);
+                        chmin(dp[v][j + k][1], min(dp[u][k][0], dp[u][k][1]) + dp[v][j][1]);
+                    }
+                }
+                curr += sz[u];
+            }
+        };
+        dfs(dfs, 1, 0);
+    }
+
+    for (int i = n; ~i; --i) {
+        if (min(dp[1][i][0], dp[1][i][1]) <= tot) {
+            cout << i << '\n';
+            return;
+        }
+    }
+
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/cf-830c.cc b/src/bin/cf-830c.cc
new file mode 100644
index 0000000..177cf9e
--- /dev/null
+++ b/src/bin/cf-830c.cc
@@ -0,0 +1,636 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, n);
+    read(ll, k);
+    readvec(int, a, n);
+
+    map<int, vector<int>, greater<>> events;
+    for (int i = 0; i < n; ++i) {
+        int x = a[i];
+        for (ll l = 1, r; l <= x; l = r + 1) {
+            ll val = (x + l - 1) / l;
+            r = val == 1 ? x : (x - 1) / (val - 1);
+            if (val > 1) {
+                events[r].emplace_back(i);
+            }
+        }
+    }
+
+    int mx = *max_element(a.begin(), a.end());
+    ll sum = accumulate(a.begin(), a.end(), ll(0));
+    ll tot = ll(1) * mx * n - sum;
+
+    if (tot <= k) {
+        ll extra = (k - tot) / n;
+        cout << mx + extra << '\n';
+        // debug(1);
+        return;
+    }
+
+    vector<int> last(n, mx + 1);
+    tot = ll(1) * (mx + 1) * n;
+
+    vector<int> diff(n, 1);
+    ll tot_diff = n;
+
+    int lastpos = mx + 1;
+    while (events.size()) {
+        auto [r, v] = *events.begin();
+        // deb(r, v);
+        tot -= tot_diff * (lastpos - r);
+        lastpos = r;
+        for (auto&& i : v) {
+            tot -= (diff[i] == 1 ? last[i] : ll(1) * diff[i] * last[i]) - ll(1) * diff[i] * (last[i] - r);
+            tot_diff -= diff[i];
+            diff[i] = (a[i] + r - 1) / r;
+            tot_diff += diff[i];
+            tot += ll(1) * diff[i] * r;
+            last[i] = r;
+        }
+        // debug(tot);
+        // debug(diff);
+        events.erase(events.begin());
+        // debugvec(events);
+        if (events.empty()) {
+            cout << 1 << '\n';
+            return;
+        } else if (tot_diff != 0) {
+            int nxt = events.begin()->first;
+            ll t = (tot - sum - k + tot_diff - 1) / tot_diff;
+            if (r - t > nxt) {
+                // deb(r, t, nxt);
+                cout << r - t << '\n';
+                return;
+            }
+        }
+    }
+
+    assert(false);
+
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/d.cc b/src/bin/d.cc
index 1a7e0e4..0c0583a 100644
--- a/src/bin/d.cc
+++ b/src/bin/d.cc
@@ -25,7 +25,7 @@ using ull = unsigned long long;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
-using ld = long double;
+using ld = __float128;  // up to 1e-9 precision in binary search
 using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
 using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
 using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
@@ -48,6 +48,7 @@ constexpr int INF = 0x3f3f3f3f;
 constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
 constexpr ll MDL = 1e9 + 7;
 constexpr ll PRIME = 998'244'353;
+constexpr ll PRIMELL = 901017227882342239LL;
 constexpr ll MDL1 = 8784491;
 constexpr ll MDL2 = PRIME;
 constexpr int128 INT128_MAX = numeric_limits<int128>::max();
@@ -96,9 +97,9 @@ struct igt {
 
 /* 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;)
+#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 {
@@ -132,13 +133,15 @@ struct pair_hash {
 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 {
+    safe_hash hasher;
     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;
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * pw2) % __array_hash_mdl2;
             pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
             pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
         }
@@ -173,7 +176,7 @@ template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, s
 /* io */
 #define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
 
-// add declarations to avoid cyclic dependency
+// add declarations to avoid circular dependency
 template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
 template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
 template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
@@ -239,14 +242,14 @@ std::ostream& operator<<(std::ostream& dest, const int128& value) {
 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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
-#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : a) cin >> x;)
-#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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 readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
 #define deb(...) debug(make_tuple(__VA_ARGS__))
 
 /* pops */
@@ -293,7 +296,7 @@ ll qpow(ll b, ll p, ll mod) {
 #pragma GCC diagnostic ignored "-Wparentheses"
 // Accurately find `i` 'th root of `n` (taking the floor)
 inline ll root(ll n, ll i) {
-    ll l = 0, r = pow(LLONG_MAX, ld(1) / i);
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
     while (l < r) {
         ll mid = l + r + 1 >> 1;
         if (qpow<int128>(mid, i) <= n) {
@@ -393,7 +396,7 @@ vector<int> calc_z(string t) {  // z function of t
     }
     return z;
 }
-vector<int> kmp(string s, string t) {  // find all t in s
+vector<int> kmp(const string& s, const string& t) {  // find all t in s
     string cur = t + '#' + s;
     int sz1 = s.size(), sz2 = t.size();
     vector<int> v;
@@ -403,7 +406,7 @@ vector<int> kmp(string s, string t) {  // find all t in s
     }
     return v;
 }
-int period(string s) {  // find the length of shortest recurring period
+int period(const 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) {
@@ -421,8 +424,8 @@ template <ll mdl> struct MLL {
     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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
@@ -524,7 +527,7 @@ constexpr std::array<T, N> __initarray(const T& value) {
 }
 /*******************************************************/
 
-// #define SINGLE_TEST_CASE
+#define SINGLE_TEST_CASE
 // #define DUMP_TEST_CASE 7219
 // #define TOT_TEST_CASE 10000
 
@@ -532,25 +535,7 @@ void dump() {}
 
 void dump_ignore() {}
 
-constexpr int N = 4e5 + 10;
-bool not_prime[N + 1];
-
-void soe(int n) {
-    vector<int> res;
-    for (int i = 2; i <= n; ++i) {
-        if (not not_prime[i]) {
-            res.emplace_back(i);
-        }
-        for (auto&& x : res) {
-            if (i * x > n) break;
-            not_prime[i * x] = 1;
-            if (i % x == 0) break;
-        }
-    }
-}
-
 void prep() {
-    soe(N);
 }
 
 // __attribute__((target("popcnt")))
@@ -561,44 +546,87 @@ void solve() {
         read(int, u, v);
         edge(ch, u, v);
     }
-    array<vector<int>, 2> bk;
-    vector<int> fa(n + 1);
+
+    vector<int> sz(n + 1);
     {
-        auto dfs = [&] (auto dfs, int v, int pa, int par) -> void {
-            fa[v] = pa;
-            bk[par].emplace_back(v);
+        auto dfs = [&] (auto dfs, int v, int pa) -> void {
+            sz[v] = 1;
             for (auto&& u : ch[v]) {
                 if (u == pa) continue;
-                dfs(dfs, u, v, 1 - par);
+                dfs(dfs, u, v);
+                sz[v] += sz[u];
             }
         };
-        dfs(dfs, 1, 0, 0);
+        dfs(dfs, 1, 0);
     }
-    vector<int> res(n + 1);
-    int curr = 2;
-    for (auto&& v : bk[0]) {
-        res[v] = curr;
-        curr += 2;
+
+    vector<pll> down(n + 1);
+    {
+        auto dfs = [&] (auto dfs, int v, int pa) -> void {
+            down[v].second = sz[v] - 1;
+            int tot_sz = 0;
+            for (auto&& u : ch[v]) {
+                if (u == pa) continue;
+                dfs(dfs, u, v);
+                down[v].first += down[u].first + down[u].second;
+                down[v].second += down[u].second;
+                down[v].second += ll(1) * tot_sz * sz[u];
+                tot_sz += sz[u];
+            }
+        };
+        dfs(dfs, 1, 0);
     }
-    curr = 2 * n;
-    for (auto&& v : bk[1]) {
-        res[v] = curr;
-        curr -= 2;
-    }
-    for (int i = 2; i <= n; ++i) {
-        if (abs(res[fa[i]] - res[i]) == 2) {
-            res[i] = res[fa[i]] > res[i] ? res[i] + 1 : res[i] - 1;
-            break;
-        }
+
+    vector<pll> up(n + 1);
+    {
+        auto dfs = [&] (auto dfs, int v, int pa) -> void {
+            // up[v].second += n - sz[v];
+            for (auto&& u : ch[v]) {
+                if (u == pa) continue;
+                // up[v].first += down[u].first;
+                // up[v].second += down[u].second;
+            }
+            up[v].second += n - sz[v];
+            up[v].second += ll(1) * (n - sz[v]) * (sz[v] - 1);
+            // if (v == 1) {
+            //     debug(up[v]);
+            //     debug(down[v]);
+            // }
+            for (auto&& u : ch[v]) {
+                if (u == pa) continue;
+                up[v].second -= ll(1) * sz[u] * (n - sz[v]);
+                down[v].second -= ll(1) * sz[u] * (sz[v] - sz[u]);
+                down[v].first -= down[u].first + down[u].second;
+                down[v].second -= down[u].second;
+                // if (v == 1) {
+                //     debug(u);
+                //     debug(up[v]);
+                //     debug(down[v]);
+                // }
+
+                up[u].first += up[v].first + up[v].second;
+                up[u].first += down[v].first + down[v].second;
+                up[u].second += up[v].second;
+                up[u].second += down[v].second;
+                dfs(dfs, u, v);
+
+                up[v].second += ll(1) * sz[u] * (n - sz[v]);
+                down[v].second += ll(1) * sz[u] * (sz[v] - sz[u]);
+                down[v].first += down[u].first + down[u].second;
+                down[v].second += down[u].second;
+            }
+        };
+        dfs(dfs, 1, 0);
     }
+
     for (int i = 1; i <= n; ++i) {
-        cout << res[i] << " \n"[i == n];
+        cout << up[i].first + down[i].first << '\n';
     }
 }
 
 int main() {
 #if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
-    assert(false && "incompatible compiler variant detected.");
+    static_assert(false, "incompatible compiler variant detected.");
 #endif
     untie;
     prep();
diff --git a/src/bin/g.cc b/src/bin/g.cc
index 55ee89f..aea29ad 100644
--- a/src/bin/g.cc
+++ b/src/bin/g.cc
@@ -1,5 +1,5 @@
 // #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
-#pragma GCC optimize("Ofast")
+#pragma GCC optimize("Ofast,unroll-loops")
 /************* This code requires C++17. ***************/
 
 #include<bits/stdc++.h>
@@ -25,7 +25,7 @@ using ull = unsigned long long;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
-using ld = long double;
+using ld = __float128;  // up to 1e-9 precision in binary search
 using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
 using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
 using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
@@ -48,6 +48,7 @@ constexpr int INF = 0x3f3f3f3f;
 constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
 constexpr ll MDL = 1e9 + 7;
 constexpr ll PRIME = 998'244'353;
+constexpr ll PRIMELL = 901017227882342239LL;
 constexpr ll MDL1 = 8784491;
 constexpr ll MDL2 = PRIME;
 constexpr int128 INT128_MAX = numeric_limits<int128>::max();
@@ -96,9 +97,9 @@ struct igt {
 
 /* 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;)
+#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 {
@@ -132,13 +133,15 @@ struct pair_hash {
 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 {
+    safe_hash hasher;
     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;
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * pw2) % __array_hash_mdl2;
             pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
             pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
         }
@@ -173,7 +176,7 @@ template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, s
 /* io */
 #define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
 
-// add declarations to avoid cyclic dependency
+// add declarations to avoid circular dependency
 template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
 template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
 template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
@@ -239,14 +242,14 @@ std::ostream& operator<<(std::ostream& dest, const int128& value) {
 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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
-#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : a) cin >> x;)
-#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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 readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
 #define deb(...) debug(make_tuple(__VA_ARGS__))
 
 /* pops */
@@ -289,11 +292,11 @@ ll qpow(ll b, ll p, ll mod) {
 }
 
 
-// Accurately find `i` 'th root of `n` (taking the floor)
 #pragma GCC diagnostic push
 #pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
 inline ll root(ll n, ll i) {
-    ll l = 0, r = pow(LLONG_MAX, ld(1) / i);
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
     while (l < r) {
         ll mid = l + r + 1 >> 1;
         if (qpow<int128>(mid, i) <= n) {
@@ -393,7 +396,7 @@ vector<int> calc_z(string t) {  // z function of t
     }
     return z;
 }
-vector<int> kmp(string s, string t) {  // find all t in s
+vector<int> kmp(const string& s, const string& t) {  // find all t in s
     string cur = t + '#' + s;
     int sz1 = s.size(), sz2 = t.size();
     vector<int> v;
@@ -403,7 +406,7 @@ vector<int> kmp(string s, string t) {  // find all t in s
     }
     return v;
 }
-int period(string s) {  // find the length of shortest recurring period
+int period(const 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) {
@@ -421,8 +424,8 @@ template <ll mdl> struct MLL {
     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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
@@ -524,7 +527,7 @@ constexpr std::array<T, N> __initarray(const T& value) {
 }
 /*******************************************************/
 
-// #define SINGLE_TEST_CASE
+#define SINGLE_TEST_CASE
 // #define DUMP_TEST_CASE 7219
 // #define TOT_TEST_CASE 10000
 
@@ -535,52 +538,52 @@ void dump_ignore() {}
 void prep() {
 }
 
+constexpr int M = 500;
+constexpr int N = 1e5 + 1;
+constexpr int S = 1 << 17;
+int pre[(N + M) / M][S], a[N];
+
 // __attribute__((target("popcnt")))
 void solve() {
-    read(int, n);
-    adj(ch, n);
-    for (int i = 0; i < n - 1; ++i) {
-        read(int, u, v);
-        edge(ch, u, v);
+    read(int, n, k);
+    for (int i = 0; i < n; ++i) {
+        cin >> a[i];
     }
-    vector<int> f(n + 1);
-    {
-        auto dfs = [&] (auto dfs, int v, int pa) -> void {
-            for (auto&& u : ch[v]) {
-                if (u == pa) continue;
-                dfs(dfs, u, v);
-                f[v] += 1;
+    int t = (n + M - 1) / M;
+    for (int i = 0; i < n; ++i) {
+        int c = i / M;
+        for (int j = i; j < min(n, i + M); ++j) {
+            for (int k = 0; k < S; ++k) {
+                pre[c][k] xor_eq a[j] - k;
             }
-            f[v] -= 1;
-        };
-        dfs(dfs, 1, 0);
+        }
+        i += M - 1;
     }
-    int res = 0;
-    {
-        auto dfs = [&] (auto dfs, int v, int pa, int up) -> int {
-            int curr = up + f[v];
-            int mx = curr;
-            multiset<int> sub;
-            for (auto&& u : ch[v]) {
-                if (u == pa) continue;
-                sub.emplace(dfs(dfs, u, v, curr));
-            }
-            if (sub.size()) chmax(mx, *sub.rbegin());
-            chmax(res, mx - up + 1 + (v != 1));
-            if (sub.size() >= 2) {
-                int l = *sub.rbegin(), r = *next(sub.rbegin());
-                chmax(res, (l - curr + 1) + (r - curr + 1) + (f[v] - 1) + (v != 1));
-            }
-            return mx;
-        };
-        dfs(dfs, 1, 0, 0);
+
+    while (k--) {
+        read(int, d, l, r);
+        --l, --r;
+        int left = l;
+        int res = 0;
+        while (left <= r and left % M != 0) {
+            res xor_eq a[left] - d;
+            left += 1;
+        }
+        while (r - left + 1 >= M) {
+            res xor_eq pre[left / M][d];
+            left += M;
+        }
+        for (int j = left; j <= r; ++j) {
+            res xor_eq a[j] - d;
+        }
+        cout << res << '\n';
     }
-    cout << res << '\n';
+
 }
 
 int main() {
 #if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
-    assert(false && "incompatible compiler variant detected.");
+    static_assert(false, "incompatible compiler variant detected.");
 #endif
     untie;
     prep();
diff --git a/src/bin/gym-105631a.cc b/src/bin/gym-105631a.cc
new file mode 100644
index 0000000..a3dc34e
--- /dev/null
+++ b/src/bin/gym-105631a.cc
@@ -0,0 +1,571 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, x, y, z);
+    cout << min({x / 2, y, z}) << '\n';
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/gym-105631b.cc b/src/bin/gym-105631b.cc
new file mode 100644
index 0000000..070288a
--- /dev/null
+++ b/src/bin/gym-105631b.cc
@@ -0,0 +1,576 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, n);
+    read(string, a);
+    if (a[0] == '1' or a[n - 1] == '1') {
+        cout << "Alice\n";
+    } else {
+        cout << "Bob\n";
+    }
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/gym-105631c.cc b/src/bin/gym-105631c.cc
new file mode 100644
index 0000000..592ecd7
--- /dev/null
+++ b/src/bin/gym-105631c.cc
@@ -0,0 +1,648 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+template<typename T>
+struct BIT {
+    int n;
+    vector<T> c;
+    BIT(size_t n) : n(n), c(n + 1) {}
+    void add(size_t i, const T& k) {
+        while (i <= n) {
+            c[i] += k;
+            i += lowbit(i);
+        }
+    }
+    T getsum(size_t i) {
+        T res = {};
+        while (i) {
+            res += c[i];
+            i -= lowbit(i);
+        }
+        return res;
+    }
+};
+
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, n, m);
+    n += 1;
+    vector cntrj(n, vector<int>(26));
+    vector ac(n, vector<bool>(26));
+    vector<pil> status(n);
+
+    vector<tuple<string, int, ll, int>> events;
+    vector<ll> oc = { ll(26) << 32 };
+    for (int i = 0; i < m; ++i) {
+        ll time = 0;
+        read(string, raw_time);
+        time += stoi(raw_time.substr(0, 2)) * 60 + stoi(raw_time.substr(3, 2));
+        read(int, team);
+        read(char, raw_no);
+        int no = raw_no - 'A';
+        read(string, raw_stat);
+        int stat = raw_stat == "AC";
+        bool upd = team == 0 and stat and not ac[team][no];
+        if (stat) {
+            if (ac[team][no]) {
+                ;;
+            } else {
+                ac[team][no] = 1;
+                status[team].first += 1;
+                status[team].second += time + ll(1) * 20 * cntrj[team][no];
+            }
+        } else {
+            cntrj[team][no] += 1;
+        }
+        // deb(team, status[team]);
+        ll currstatus = (26 - ll(1) * status[team].first) << 32 bitor status[team].second;
+        oc.emplace_back(currstatus);
+        events.emplace_back(raw_time, team, currstatus, upd ? no : -1);
+    }
+
+    sort(oc.begin(), oc.end());
+    int t = unique(oc.begin(), oc.end()) - oc.begin();
+    oc.resize(t);
+    auto get = [&] (ll x) { return lower_bound(oc.begin(), oc.end(), x) - oc.begin(); };
+
+    BIT<int> tr(t);
+
+    vector<ll> curr(n, (ll(1) * 26) << 32);
+    tr.add((ll(1) * 26) << 32, n);
+
+    for (auto&& [raw_time, team, penalty, no] : events) {
+        int old;
+        if (no != -1) {
+            old = tr.getsum(get(curr[0])) + 1;
+        }
+        tr.add(get(curr[team]) + 1, -1);
+        curr[team] = penalty;
+        tr.add(get(curr[team]) + 1, 1);
+        if (no != -1) {
+            cout << raw_time << ' ' << char(no + 'A') << " #" << old << " -> #" << tr.getsum(get(curr[0])) + 1 << '\n';
+        }
+    }
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/gym-105631d.cc b/src/bin/gym-105631d.cc
new file mode 100644
index 0000000..0c0583a
--- /dev/null
+++ b/src/bin/gym-105631d.cc
@@ -0,0 +1,651 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, n);
+    adj(ch, n);
+    for (int i = 0; i < n - 1; ++i) {
+        read(int, u, v);
+        edge(ch, u, v);
+    }
+
+    vector<int> sz(n + 1);
+    {
+        auto dfs = [&] (auto dfs, int v, int pa) -> void {
+            sz[v] = 1;
+            for (auto&& u : ch[v]) {
+                if (u == pa) continue;
+                dfs(dfs, u, v);
+                sz[v] += sz[u];
+            }
+        };
+        dfs(dfs, 1, 0);
+    }
+
+    vector<pll> down(n + 1);
+    {
+        auto dfs = [&] (auto dfs, int v, int pa) -> void {
+            down[v].second = sz[v] - 1;
+            int tot_sz = 0;
+            for (auto&& u : ch[v]) {
+                if (u == pa) continue;
+                dfs(dfs, u, v);
+                down[v].first += down[u].first + down[u].second;
+                down[v].second += down[u].second;
+                down[v].second += ll(1) * tot_sz * sz[u];
+                tot_sz += sz[u];
+            }
+        };
+        dfs(dfs, 1, 0);
+    }
+
+    vector<pll> up(n + 1);
+    {
+        auto dfs = [&] (auto dfs, int v, int pa) -> void {
+            // up[v].second += n - sz[v];
+            for (auto&& u : ch[v]) {
+                if (u == pa) continue;
+                // up[v].first += down[u].first;
+                // up[v].second += down[u].second;
+            }
+            up[v].second += n - sz[v];
+            up[v].second += ll(1) * (n - sz[v]) * (sz[v] - 1);
+            // if (v == 1) {
+            //     debug(up[v]);
+            //     debug(down[v]);
+            // }
+            for (auto&& u : ch[v]) {
+                if (u == pa) continue;
+                up[v].second -= ll(1) * sz[u] * (n - sz[v]);
+                down[v].second -= ll(1) * sz[u] * (sz[v] - sz[u]);
+                down[v].first -= down[u].first + down[u].second;
+                down[v].second -= down[u].second;
+                // if (v == 1) {
+                //     debug(u);
+                //     debug(up[v]);
+                //     debug(down[v]);
+                // }
+
+                up[u].first += up[v].first + up[v].second;
+                up[u].first += down[v].first + down[v].second;
+                up[u].second += up[v].second;
+                up[u].second += down[v].second;
+                dfs(dfs, u, v);
+
+                up[v].second += ll(1) * sz[u] * (n - sz[v]);
+                down[v].second += ll(1) * sz[u] * (sz[v] - sz[u]);
+                down[v].first += down[u].first + down[u].second;
+                down[v].second += down[u].second;
+            }
+        };
+        dfs(dfs, 1, 0);
+    }
+
+    for (int i = 1; i <= n; ++i) {
+        cout << up[i].first + down[i].first << '\n';
+    }
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/gym-105631g.cc b/src/bin/gym-105631g.cc
new file mode 100644
index 0000000..aea29ad
--- /dev/null
+++ b/src/bin/gym-105631g.cc
@@ -0,0 +1,608 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+constexpr int M = 500;
+constexpr int N = 1e5 + 1;
+constexpr int S = 1 << 17;
+int pre[(N + M) / M][S], a[N];
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, n, k);
+    for (int i = 0; i < n; ++i) {
+        cin >> a[i];
+    }
+    int t = (n + M - 1) / M;
+    for (int i = 0; i < n; ++i) {
+        int c = i / M;
+        for (int j = i; j < min(n, i + M); ++j) {
+            for (int k = 0; k < S; ++k) {
+                pre[c][k] xor_eq a[j] - k;
+            }
+        }
+        i += M - 1;
+    }
+
+    while (k--) {
+        read(int, d, l, r);
+        --l, --r;
+        int left = l;
+        int res = 0;
+        while (left <= r and left % M != 0) {
+            res xor_eq a[left] - d;
+            left += 1;
+        }
+        while (r - left + 1 >= M) {
+            res xor_eq pre[left / M][d];
+            left += M;
+        }
+        for (int j = left; j <= r; ++j) {
+            res xor_eq a[j] - d;
+        }
+        cout << res << '\n';
+    }
+
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/gym-105631j.cc b/src/bin/gym-105631j.cc
new file mode 100644
index 0000000..1a62b1a
--- /dev/null
+++ b/src/bin/gym-105631j.cc
@@ -0,0 +1,590 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+// #define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, n);
+    read(ll, l);
+    readvec(ll, a, n);
+    ll raw = 0;
+    for (int i = 0; i < n; ++i) {
+        raw or_eq a[i];
+    }
+    for (int i = 60; ~i; --i) {
+        int cnt = 0;
+        for (int j = 0; j < n; ++j) {
+            cnt += a[j] >> i bitand 1;
+        }
+        if (cnt < 2) continue;
+        for (int j = 0; j < n; ++j) {
+            if ((a[j] >> i bitand 1) and ((a[j] bitor ((ll(1) << i) - 1)) xor ll(1) << i) >= l) {
+                cout << (raw bitor ((ll(1) << i) - 1)) << '\n';
+                return;
+            }
+        }
+    }
+    cout << raw << '\n';
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/gym-105631k.cc b/src/bin/gym-105631k.cc
new file mode 100644
index 0000000..fc1bf1f
--- /dev/null
+++ b/src/bin/gym-105631k.cc
@@ -0,0 +1,586 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, n, m);
+    if (m == 1) {
+        cout << 0 << '\n';
+        return;
+    }
+    vector<ll> md(n + 1);
+    for (int i = 1; i <= n; ++i) {
+        md[i] = qpow(i, m, PRIME);
+    }
+    ll res = 0;
+    for (int i = 1; i < n; ++i) {
+        ll all = md[i + 1];
+        ll one = 2 * md[i] % PRIME;
+        ll none = i - 1 <= 0 ? 0 : md[i - 1];
+        res += ll(1) * ((n - i) * mod(all - one + none, PRIME) % PRIME) * (ll(1) * i * i % PRIME) % PRIME;
+        res %= PRIME;
+    }
+    cout << res << '\n';
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/gym-105631l.cc b/src/bin/gym-105631l.cc
new file mode 100644
index 0000000..9fe9dcd
--- /dev/null
+++ b/src/bin/gym-105631l.cc
@@ -0,0 +1,627 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, n, m);
+    readvec(int, a, n);
+    readvec(int, b, m);
+
+    vector res(n, vector<int>(m));
+    for (int i = 0; i < n; ++i) {
+        for (int j = 0; j < m; ++j) {
+            res[i][j] = b[j];
+        }
+    }
+    int g = 0;
+    for (int i = 0; i < n; ++i) {
+        g = g == 0 ? a[i] : gcd(g, a[i]);
+    }
+    ll l = 1;
+    for (int j = 0; j < m; ++j) {
+        l = lcm(l, ll(1) * b[j]);
+        if (l > 1e9) {
+            cout << "No\n";
+            return;
+        }
+    }
+    if (g % l != 0) {
+        cout << "No\n";
+        return;
+    }
+    int col = 0, dir = 1;
+    for (int i = 0; i < n; ++i) {
+        if (l == a[i]) continue;
+        res[i][col] = a[i];
+        col += dir;
+        if (col == m) {
+            col = max(0, m - 2);
+            dir = -dir;
+        } else if (col == -1) {
+            col = min(m - 1, 1);
+            dir = -dir;
+        }
+    }
+
+    for (int j = 0; j < m; ++j) {
+        int g = 0;
+        for (int i = 0; i < n; ++i) {
+            g = g == 0 ? res[i][j] : gcd(g, res[i][j]);
+        }
+        if (g != b[j]) {
+            cout << "No\n";
+            return;
+        }
+    }
+
+    cout << "Yes\n";
+    for (int i = 0; i < n; ++i) {
+        for (int j = 0; j < m; ++j) {
+            cout << res[i][j] << ' ';
+        }
+        cout << '\n';
+    }
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/j.cc b/src/bin/j.cc
index c807c2d..1a62b1a 100644
--- a/src/bin/j.cc
+++ b/src/bin/j.cc
@@ -1,5 +1,5 @@
 // #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
-#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
+#pragma GCC optimize("Ofast,unroll-loops")
 /************* This code requires C++17. ***************/
 
 #include<bits/stdc++.h>
@@ -12,6 +12,8 @@ using namespace std;
 constexpr void __() {}
 #define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
 #define __as_typeof(container) remove_reference<decltype(container)>::type
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
 
 /* type aliases */
 #if LONG_LONG_MAX != INT64_MAX
@@ -23,7 +25,7 @@ using ull = unsigned long long;
 #endif
 using int128 = __int128_t;
 using uint128 = __uint128_t;
-using ld = long double;
+using ld = __float128;  // up to 1e-9 precision in binary search
 using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
 using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
 using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
@@ -46,6 +48,7 @@ constexpr int INF = 0x3f3f3f3f;
 constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
 constexpr ll MDL = 1e9 + 7;
 constexpr ll PRIME = 998'244'353;
+constexpr ll PRIMELL = 901017227882342239LL;
 constexpr ll MDL1 = 8784491;
 constexpr ll MDL2 = PRIME;
 constexpr int128 INT128_MAX = numeric_limits<int128>::max();
@@ -94,9 +97,9 @@ struct igt {
 
 /* 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;)
+#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 {
@@ -130,13 +133,15 @@ struct pair_hash {
 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 {
+    safe_hash hasher;
     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;
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * pw2) % __array_hash_mdl2;
             pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
             pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
         }
@@ -170,6 +175,17 @@ template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, s
 
 /* io */
 #define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
 template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
     return in >> p.first >> p.second;
 }
@@ -177,6 +193,14 @@ template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T,
     out << "{" << p.first << ", " << p.second << "}";
     return out;
 }
+template<typename T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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
@@ -217,21 +241,36 @@ std::ostream& operator<<(std::ostream& dest, const int128& value) {
 }
 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 read(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
 #define deb(...) debug(make_tuple(__VA_ARGS__))
 
 /* 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();)
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
 
 /* math */
 template <typename return_t>
@@ -243,11 +282,43 @@ return_t qpow(ll b, ll p) {
     else return half * half;
 }
 
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
 #define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
 #define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
 
+__attribute__((target("lzcnt")))
 constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
 
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
 void __exgcd(ll a, ll b, ll& x, ll& y) {
   if (b == 0) {
     x = 1, y = 0;
@@ -298,15 +369,15 @@ vector<pii> decompose_prime(int N) {
 
 /* 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;
+    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();
@@ -325,17 +396,17 @@ vector<int> calc_z(string t) {  // z function of t
     }
     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;
+vector<int> kmp(const string& s, const 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 period(const 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) {
@@ -353,16 +424,16 @@ template <ll mdl> struct MLL {
     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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
 };
 
 template <ll mdl>
@@ -456,7 +527,7 @@ constexpr std::array<T, N> __initarray(const T& value) {
 }
 /*******************************************************/
 
-#define SINGLE_TEST_CASE
+// #define SINGLE_TEST_CASE
 // #define DUMP_TEST_CASE 7219
 // #define TOT_TEST_CASE 10000
 
@@ -470,28 +541,31 @@ void prep() {
 // __attribute__((target("popcnt")))
 void solve() {
     read(int, n);
-    ll tot = 0;
+    read(ll, l);
+    readvec(ll, a, n);
+    ll raw = 0;
     for (int i = 0; i < n; ++i) {
-        read(char, c);
-        if (c == 'B') {
-            read(int, x);
-            ll use = min<ll>(x, tot);
-            tot -= use;
-            if (x - use > 0) {
-                cout << "YES\n";
-            } else {
-                cout << "NO\n";
+        raw or_eq a[i];
+    }
+    for (int i = 60; ~i; --i) {
+        int cnt = 0;
+        for (int j = 0; j < n; ++j) {
+            cnt += a[j] >> i bitand 1;
+        }
+        if (cnt < 2) continue;
+        for (int j = 0; j < n; ++j) {
+            if ((a[j] >> i bitand 1) and ((a[j] bitor ((ll(1) << i) - 1)) xor ll(1) << i) >= l) {
+                cout << (raw bitor ((ll(1) << i) - 1)) << '\n';
+                return;
             }
-        } else {
-            read(int, x);
-            tot += x;
         }
     }
+    cout << raw << '\n';
 }
 
 int main() {
 #if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
-    assert(false && "incompatible compiler variant detected.");
+    static_assert(false, "incompatible compiler variant detected.");
 #endif
     untie;
     prep();
diff --git a/src/bin/k.cc b/src/bin/k.cc
new file mode 100644
index 0000000..fc1bf1f
--- /dev/null
+++ b/src/bin/k.cc
@@ -0,0 +1,586 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {}
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, n, m);
+    if (m == 1) {
+        cout << 0 << '\n';
+        return;
+    }
+    vector<ll> md(n + 1);
+    for (int i = 1; i <= n; ++i) {
+        md[i] = qpow(i, m, PRIME);
+    }
+    ll res = 0;
+    for (int i = 1; i < n; ++i) {
+        ll all = md[i + 1];
+        ll one = 2 * md[i] % PRIME;
+        ll none = i - 1 <= 0 ? 0 : md[i - 1];
+        res += ll(1) * ((n - i) * mod(all - one + none, PRIME) % PRIME) * (ll(1) * i * i % PRIME) % PRIME;
+        res %= PRIME;
+    }
+    cout << res << '\n';
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/l.cc b/src/bin/l.cc
new file mode 100644
index 0000000..9fe9dcd
--- /dev/null
+++ b/src/bin/l.cc
@@ -0,0 +1,627 @@
+// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
+#pragma GCC optimize("Ofast,unroll-loops")
+/************* This code 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
+template <typename T> struct argument_type;
+template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
+
+/* 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;
+#endif
+using int128 = __int128_t;
+using uint128 = __uint128_t;
+using ld = __float128;  // up to 1e-9 precision in binary search
+using pii = pair<int, int>;           using pil = pair<int, ll>;           using pid = pair<int, ld>;
+using pli = pair<ll, int>;            using pll = pair<ll, ll>;            using pld = pair<ll, ld>;
+using pdi = pair<ld, int>;            using pdl = pair<ld, ll>;            using pdd = pair<ld, ld>;
+using tiii = tuple<int, int, int>;    using tiil = tuple<int, int, ll>;    using tiid = tuple<int, int, ld>;
+using tili = tuple<int, ll, int>;     using till = tuple<int, ll, ll>;     using tild = tuple<int, ll, ld>;
+using tidi = tuple<int, ld, int>;     using tidl = tuple<int, ld, ll>;     using tidd = tuple<int, ld, ld>;
+using tlii = tuple<ll, int, int>;     using tlil = tuple<ll, int, ll>;     using tlid = tuple<ll, int, ld>;
+using tlli = tuple<ll, ll, int>;      using tlll = tuple<ll, ll, ll>;      using tlld = tuple<ll, ll, ld>;
+using tldi = tuple<ll, ld, int>;      using tldl = tuple<ll, ld, ll>;      using tldd = tuple<ll, ld, ld>;
+using tdii = tuple<ld, int, int>;     using tdil = tuple<ld, int, ll>;     using tdid = tuple<ld, int, ld>;
+using tdli = tuple<ld, ll, int>;      using tdll = tuple<ld, ll, ll>;      using tdld = tuple<ld, ll, ld>;
+using tddi = tuple<ld, ld, int>;      using tddl = tuple<ld, ld, ll>;      using tddd = tuple<ld, ld, ld>;
+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 PRIMELL = 901017227882342239LL;
+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_64 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 {
+    safe_hash hasher;
+    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) {
+            auto h = hasher(x);
+            res1 = (res1 + h * pw1) % __array_hash_mdl1;
+            res2 = (res2 + h * 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 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, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
+#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
+#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
+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))
+
+// add declarations to avoid circular dependency
+template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
+template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
+template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
+template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
+template<typename Char, typename Traits, typename... Args>
+decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
+template<typename T> ostream& operator<<(ostream&, const vector<T>&);
+std::ostream& operator<<(std::ostream&, const int128&);
+
+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 T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
+    for (size_t i = 0; i < N; ++i) in >> a[i];
+    return in;
+}
+template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
+    for (auto&& i : a) out << i << ' ';
+    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;
+}
+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(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
+#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
+#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::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;)
+#define deb(...) debug(make_tuple(__VA_ARGS__))
+
+/* pops */
+template <typename Container>
+inline auto poptop(Container& q) {
+    auto ret = q.top();
+    q.pop();
+    return ret;
+}
+template <typename Container>
+inline auto popback(Container& q) {
+    auto ret = q.back();
+    q.pop_back();
+    return ret;
+}
+template <typename Container>
+inline auto popfront(Container& q) {
+    auto ret = q.front();
+    q.pop_front();
+    return ret;
+}
+
+/* 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;
+}
+
+// dynamic modulus
+ll qpow(ll b, ll p, ll mod) {
+    if (b == 0 and p != 0) return 0;
+    if (p == 0) return 1;
+    ll half = qpow(b, p / 2, mod);
+    if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
+    else return half * half % mod;
+}
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wparentheses"
+// Accurately find `i` 'th root of `n` (taking the floor)
+inline ll root(ll n, ll i) {
+    ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
+    while (l < r) {
+        ll mid = l + r + 1 >> 1;
+        if (qpow<int128>(mid, i) <= n) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+#pragma GCC diagnostic pop
+
+
+#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
+#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
+
+__attribute__((target("lzcnt")))
+constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
+
+template <typename T>
+T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
+
+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(const string& s, const 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(const 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(int128(lhs.val) * rhs.val, mdl); }
+    friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, 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; }
+    MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
+    MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
+    MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
+    MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
+    MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
+};
+
+template <ll mdl>
+ostream& operator<<(ostream& out, const MLL<mdl>& num) {
+    return out << num.val;
+}
+
+template <ll mdl>
+istream& operator>>(istream& in, MLL<mdl>& num) {
+    return in >> num.val;
+}
+
+// miscancellous
+template <typename T, typename U>
+bool chmax(T& lhs, const U& rhs) {
+    bool ret = lhs < rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+template <typename T, typename U>
+bool chmin(T& lhs, const U& rhs) {
+    bool ret = lhs > rhs;
+    if (ret) {
+        lhs = rhs;
+    }
+    return ret;
+}
+
+#define functor(func) ([&](auto&&... val) \
+noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
+{return func(std::forward<decltype(val)>(val)...);})
+#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
+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 initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
+namespace detail {
+    template <typename T, std::size_t...Is>
+    constexpr std::array<T, sizeof...(Is)>
+    make_array(const T& value, std::index_sequence<Is...>) {
+        return {{(static_cast<void>(Is), value)...}};
+    }
+}
+
+template <typename T, std::size_t N>
+constexpr std::array<T, N> __initarray(const T& value) {
+    return detail::make_array(value, std::make_index_sequence<N>());
+}
+/*******************************************************/
+
+#define SINGLE_TEST_CASE
+// #define DUMP_TEST_CASE 7219
+// #define TOT_TEST_CASE 10000
+
+void dump() {}
+
+void dump_ignore() {}
+
+void prep() {
+}
+
+// __attribute__((target("popcnt")))
+void solve() {
+    read(int, n, m);
+    readvec(int, a, n);
+    readvec(int, b, m);
+
+    vector res(n, vector<int>(m));
+    for (int i = 0; i < n; ++i) {
+        for (int j = 0; j < m; ++j) {
+            res[i][j] = b[j];
+        }
+    }
+    int g = 0;
+    for (int i = 0; i < n; ++i) {
+        g = g == 0 ? a[i] : gcd(g, a[i]);
+    }
+    ll l = 1;
+    for (int j = 0; j < m; ++j) {
+        l = lcm(l, ll(1) * b[j]);
+        if (l > 1e9) {
+            cout << "No\n";
+            return;
+        }
+    }
+    if (g % l != 0) {
+        cout << "No\n";
+        return;
+    }
+    int col = 0, dir = 1;
+    for (int i = 0; i < n; ++i) {
+        if (l == a[i]) continue;
+        res[i][col] = a[i];
+        col += dir;
+        if (col == m) {
+            col = max(0, m - 2);
+            dir = -dir;
+        } else if (col == -1) {
+            col = min(m - 1, 1);
+            dir = -dir;
+        }
+    }
+
+    for (int j = 0; j < m; ++j) {
+        int g = 0;
+        for (int i = 0; i < n; ++i) {
+            g = g == 0 ? res[i][j] : gcd(g, res[i][j]);
+        }
+        if (g != b[j]) {
+            cout << "No\n";
+            return;
+        }
+    }
+
+    cout << "Yes\n";
+    for (int i = 0; i < n; ++i) {
+        for (int j = 0; j < m; ++j) {
+            cout << res[i][j] << ' ';
+        }
+        cout << '\n';
+    }
+}
+
+int main() {
+#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
+    static_assert(false, "incompatible compiler variant detected.");
+#endif
+    untie;
+    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
+}
diff --git a/src/bin/std.in b/src/bin/std.in
index 5693fed..4df20da 100644
--- a/src/bin/std.in
+++ b/src/bin/std.in
@@ -1 +1,7 @@
-aaaaaaaaaa

+6 16
+10 9
+10 5 1
+12 2 1
+20 18 3
+10 2 3
+2 1 5
diff --git a/src/bin/test.py b/src/bin/test.py
index ac433d4..b9ddb1f 100644
--- a/src/bin/test.py
+++ b/src/bin/test.py
@@ -8,8 +8,10 @@ import io
 PRIME = 998_244_353
 
 if __name__ == '__main__':
-    N = 50
-    print(N)
+    N = 5000
+    M = 10 ** 9
+    print(N, M)
+    print(10, 9)
     for i in range(2, N + 1):
-        print(f'{randint(1, i - 1)} {i} {randint(100000000, 999999999)}')
-    print(f'1 50 {randint(100000000, 999999999)}')
+        print(10, 9, 1)
+