結果
問題 | No.2459 Stampaholic (Hard) |
ユーザー |
|
提出日時 | 2023-09-02 06:37:47 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 31,084 bytes |
コンパイル時間 | 4,206 ms |
コンパイル使用メモリ | 382,012 KB |
実行使用メモリ | 53,604 KB |
最終ジャッジ日時 | 2024-06-11 13:30:34 |
合計ジャッジ時間 | 6,485 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 1 WA * 2 |
other | AC * 7 WA * 12 |
ソースコード
#include <bits/stdc++.h>#include <x86intrin.h>using namespace std;using namespace numbers;using uint = unsigned int;template<uint _mod>struct modular_fixed_base{static constexpr uint mod(){return _mod;}template<class T>static vector<modular_fixed_base> precalc_power(T base, int SZ){vector<modular_fixed_base> res(SZ + 1, 1);for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;return res;}static vector<modular_fixed_base> _INV;static void precalc_inverse(int SZ){if(_INV.empty()) _INV.assign(2, 1);for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]);}// _mod must be a primestatic modular_fixed_base _primitive_root;static modular_fixed_base primitive_root(){if(_primitive_root) return _primitive_root;if(_mod == 2) return _primitive_root = 1;if(_mod == 998244353) return _primitive_root = 3;uint divs[20] = {};divs[0] = 2;int cnt = 1;uint x = (_mod - 1) / 2;while(x % 2 == 0) x /= 2;for(auto i = 3; 1LL * i * i <= x; i += 2){if(x % i == 0){divs[cnt ++] = i;while(x % i == 0) x /= i;}}if(x > 1) divs[cnt ++] = x;for(auto g = 2; ; ++ g){bool ok = true;for(auto i = 0; i < cnt; ++ i){if((modular_fixed_base(g).power((_mod - 1) / divs[i])) == 1){ok = false;break;}}if(ok) return _primitive_root = g;}}constexpr modular_fixed_base(): data(){ }modular_fixed_base(const double &x){ data = normalize(llround(x)); }modular_fixed_base(const long double &x){ data = normalize(llround(x)); }template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base(const T &x){ data = normalize(x); }template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> static uint normalize(const T &x){int sign = x >= 0 ? 1 : -1;uint v = _mod <= sign * x ? sign * x % _mod : sign * x;if(sign == -1 && v) v = _mod - v;return v;}const uint &operator()() const{ return data; }template<class T> operator T() const{ return data; }modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; }modular_fixed_base &operator-=(const modular_fixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; }template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this +=modular_fixed_base(otr); }template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base &operator-=(const T &otr){ return *this -=modular_fixed_base(otr); }modular_fixed_base &operator++(){ return *this += 1; }modular_fixed_base &operator--(){ return *this += _mod - 1; }modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; }modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; }modular_fixed_base operator-() const{ return modular_fixed_base(_mod - data); }modular_fixed_base &operator*=(const modular_fixed_base &rhs){data = (unsigned long long)data * rhs.data % _mod;return *this;}template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr>modular_fixed_base &inplace_power(T e){if(!data) return *this = {};if(data == 1) return *this;if(data == mod() - 1) return e % 2 ? *this : *this = -*this;if(e < 0) *this = 1 / *this, e = -e;modular_fixed_base res = 1;for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;return *this = res;}template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr>modular_fixed_base power(T e) const{return modular_fixed_base(*this).inplace_power(e);}modular_fixed_base &operator/=(const modular_fixed_base &otr){int a = otr.data, m = _mod, u = 0, v = 1;if(a < _INV.size()) return *this *= _INV[a];while(a){int t = m / a;m -= t * a; swap(a, m);u -= t * v; swap(u, v);}assert(m == 1);return *this *= u;}uint data;};template<uint _mod> vector<modular_fixed_base<_mod>> modular_fixed_base<_mod>::_INV;template<uint _mod> modular_fixed_base<_mod> modular_fixed_base<_mod>::_primitive_root;template<uint _mod> bool operator==(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data == rhs.data; }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator==(const modular_fixed_base<_mod> &lhs, T rhs){return lhs == modular_fixed_base<_mod>(rhs); }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator==(T lhs, const modular_fixed_base<_mod> &rhs){return modular_fixed_base<_mod>(lhs) == rhs; }template<uint _mod> bool operator!=(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return !(lhs == rhs); }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator!=(const modular_fixed_base<_mod> &lhs, T rhs){return !(lhs == rhs); }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator!=(T lhs, const modular_fixed_base<_mod> &rhs){return !(lhs == rhs); }template<uint _mod> bool operator<(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data < rhs.data; }template<uint _mod> bool operator>(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data > rhs.data; }template<uint _mod> bool operator<=(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data <= rhs.data; }template<uint _mod> bool operator>=(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data >= rhs.data; }template<uint _mod> modular_fixed_base<_mod> operator+(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ returnmodular_fixed_base<_mod>(lhs) += rhs; }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator+(const modular_fixed_base<_mod> &lhs, T rhs){ return modular_fixed_base<_mod>(lhs) += rhs; }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator+(T lhs, constmodular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) += rhs; }template<uint _mod> modular_fixed_base<_mod> operator-(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ returnmodular_fixed_base<_mod>(lhs) -= rhs; }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator-(const modular_fixed_base<_mod> &lhs, T rhs){ return modular_fixed_base<_mod>(lhs) -= rhs; }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator-(T lhs, constmodular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) -= rhs; }template<uint _mod> modular_fixed_base<_mod> operator*(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ returnmodular_fixed_base<_mod>(lhs) *= rhs; }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator*(const modular_fixed_base<_mod> &lhs, T rhs){ return modular_fixed_base<_mod>(lhs) *= rhs; }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator*(T lhs, constmodular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) *= rhs; }template<uint _mod> modular_fixed_base<_mod> operator/(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs) { returnmodular_fixed_base<_mod>(lhs) /= rhs; }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator/(const modular_fixed_base<_mod> &lhs, T rhs) { return modular_fixed_base<_mod>(lhs) /= rhs; }template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator/(T lhs, constmodular_fixed_base<_mod> &rhs) { return modular_fixed_base<_mod>(lhs) /= rhs; }template<uint _mod> istream &operator>>(istream &in, modular_fixed_base<_mod> &number){long long x;in >> x;number.data = modular_fixed_base<_mod>::normalize(x);return in;}#define _PRINT_AS_FRACTIONtemplate<uint _mod> ostream &operator<<(ostream &out, const modular_fixed_base<_mod> &number){#if defined(LOCAL) && defined(_PRINT_AS_FRACTION)out << number();cerr << "(";for(auto d = 1; ; ++ d){if((number * d).data <= 1000000){cerr << (number * d).data << "/" << d;break;}else if((-number * d).data <= 1000000){cerr << "-" << (-number * d).data << "/" << d;break;}}cerr << ")";return out;#elsereturn out << number();#endif}#undef _PRINT_AS_FRACTION// const uint mod = 1e9 + 7; // 1000000007const uint mod = (119 << 23) + 1; // 998244353// const uint mod = 1e9 + 9; // 1000000009using modular = modular_fixed_base<mod>;template<class T>struct combinatorics{// O(n)static vector<T> precalc_fact(int n){vector<T> f(n + 1, 1);for(auto i = 1; i <= n; ++ i) f[i] = f[i - 1] * i;return f;}// O(n * m)static vector<vector<T>> precalc_C(int n, int m){vector<vector<T>> c(n + 1, vector<T>(m + 1));for(auto i = 0; i <= n; ++ i) for(auto j = 0; j <= min(i, m); ++ j) c[i][j] = i && j ? c[i - 1][j - 1] + c[i - 1][j] : T(1);return c;}int SZ = 0;vector<T> inv, fact, invfact;combinatorics(){ }// O(SZ)combinatorics(int SZ): SZ(SZ), inv(SZ + 1, 1), fact(SZ + 1, 1), invfact(SZ + 1, 1){for(auto i = 1; i <= SZ; ++ i) fact[i] = fact[i - 1] * i;invfact[SZ] = 1 / fact[SZ];for(auto i = SZ - 1; i >= 0; -- i){invfact[i] = invfact[i + 1] * (i + 1);inv[i + 1] = invfact[i + 1] * fact[i];}}// O(1)T C(int n, int k) const{return n < 0 ? C(-n + k - 1, k) * (k & 1 ? -1 : 1) : n < k || k < 0 ? T() : fact[n] * invfact[k] * invfact[n - k];}// O(1)T P(int n, int k) const{return n < k ? T() : fact[n] * invfact[n - k];}// O(1)T H(int n, int k) const{return C(n + k - 1, k);}// O(min(k, n - k))T naive_C(long long n, long long k) const{if(n < k) return 0;T res = 1;k = min(k, n - k);for(auto i = n; i > n - k; -- i) res *= i;return res * invfact[k];}// O(k)T naive_P(long long n, int k) const{if(n < k) return 0;T res = 1;for(auto i = n; i > n - k; -- i) res *= i;return res;}// O(k)T naive_H(long long n, int k) const{return naive_C(n + k - 1, k);}// O(1)bool parity_C(long long n, long long k) const{return n < k ? false : (n & k) == k;}// Number of ways to place n '('s and k ')'s starting with m copies of '(' such that in each prefix, number of '(' is equal or greater than ')'// Catalan(n, n, 0): n-th catalan number// Catalan(s, s+k-1, k-1): sum of products of k catalan numbers where the index of product sums up to s.// O(1)T Catalan(int n, int k, int m = 0) const{assert(0 <= min({n, k, m}));return k <= m ? C(n + k, n) : k <= n + m ? C(n + k, n) - C(n + k, k - m - 1) : T();}};// T must be of modular type// mod must be a prime// Requires modulartemplate<class T>struct number_theoric_transform_wrapper{// i \in [2^k, 2^{k+1}) holds w_{2^k+1}^{i-2^k}static vector<T> root, buffer1, buffer2;static void adjust_root(int n){if(root.empty()) root = {1, 1};for(auto k = (int)root.size(); k < n; k <<= 1){root.resize(n, 1);T w = T::primitive_root().power((T::mod() - 1) / (k << 1));for(auto i = k; i < k << 1; ++ i) root[i] = i & 1 ? root[i >> 1] * w : root[i >> 1];}}// n must be a power of two// p must have next n memories allocated// O(n * log(n))static void transform(int n, T *p, bool invert = false){assert(n && __builtin_popcount(n) == 1 && (T::mod() - 1) % n == 0);for(auto i = 1, j = 0; i < n; ++ i){int bit = n >> 1;for(; j & bit; bit >>= 1) j ^= bit;j ^= bit;if(i < j) swap(p[i], p[j]);}adjust_root(n);for(auto len = 1; len < n; len <<= 1) for(auto i = 0; i < n; i += len << 1) for(auto j = 0; j < len; ++ j){T x = p[i + j], y = p[len + i + j] * root[len + j];p[i + j] = x + y, p[len + i + j] = x - y;}if(invert){reverse(p + 1, p + n);T inv_n = T(1) / n;for(auto i = 0; i < n; ++ i) p[i] *= inv_n;}}static void transform(vector<T> &p, bool invert = false){transform((int)p.size(), p.data(), invert);}// Double the length of the ntt array// n must be a power of two// p must have next 2n memories allocated// O(n * log(n))static void double_up(int n, T *p){assert(n && __builtin_popcount(n) == 1 && (T().mod() - 1) % (n << 1) == 0);buffer1.resize(n << 1);for(auto i = 0; i < n; ++ i) buffer1[i << 1] = p[i];transform(n, p, true);adjust_root(n << 1);for(auto i = 0; i < n; ++ i) p[i] *= root[n | i];transform(n, p);for(auto i = 0; i < n; ++ i) buffer1[i << 1 | 1] = p[i];copy(buffer1.begin(), buffer1.begin() + 2 * n, p);}static void double_up(vector<T> &p){int n = (int)p.size();p.resize(n << 1);double_up(n, p.data());}// O(n * m)static vector<T> convolute_naive(const vector<T> &p, const vector<T> &q){vector<T> res(max((int)p.size() + (int)q.size() - 1, 0));for(auto i = 0; i < (int)p.size(); ++ i) for(auto j = 0; j < (int)q.size(); ++ j) res[i + j] += p[i] * q[j];return res;}// O((n + m) * log(n + m))static vector<T> convolute(const vector<T> &p, const vector<T> &q){if(min(p.size(), q.size()) < 55) return convolute_naive(p, q);int m = (int)p.size() + (int)q.size() - 1, n = 1 << __lg(m) + 1;buffer1.assign(n, 0);copy(p.begin(), p.end(), buffer1.begin());transform(buffer1);buffer2.assign(n, 0);copy(q.begin(), q.end(), buffer2.begin());transform(buffer2);for(auto i = 0; i < n; ++ i) buffer1[i] *= buffer2[i];transform(buffer1, true);return vector<T>(buffer1.begin(), buffer1.begin() + m);}// O((n + m) * log(n + m))static vector<T> arbitrarily_convolute(const vector<T> &p, const vector<T> &q){using modular0 = modular_fixed_base<1045430273>;using modular1 = modular_fixed_base<1051721729>;using modular2 = modular_fixed_base<1053818881>;using ntt0 = number_theoric_transform_wrapper<modular0>;using ntt1 = number_theoric_transform_wrapper<modular1>;using ntt2 = number_theoric_transform_wrapper<modular2>;vector<modular0> p0((int)p.size()), q0((int)q.size());for(auto i = 0; i < (int)p.size(); ++ i) p0[i] = p[i].data;for(auto i = 0; i < (int)q.size(); ++ i) q0[i] = q[i].data;auto xy0 = ntt0::convolute(p0, q0);vector<modular1> p1((int)p.size()), q1((int)q.size());for(auto i = 0; i < (int)p.size(); ++ i) p1[i] = p[i].data;for(auto i = 0; i < (int)q.size(); ++ i) q1[i] = q[i].data;auto xy1 = ntt1::convolute(p1, q1);vector<modular2> p2((int)p.size()), q2((int)q.size());for(auto i = 0; i < (int)p.size(); ++ i) p2[i] = p[i].data;for(auto i = 0; i < (int)q.size(); ++ i) q2[i] = q[i].data;auto xy2 = ntt2::convolute(p2, q2);static const modular1 r01 = 1 / modular1(modular0::mod());static const modular2 r02 = 1 / modular2(modular0::mod());static const modular2 r12 = 1 / modular2(modular1::mod());static const modular2 r02r12 = r02 * r12;static const T w1 = modular0::mod();static const T w2 = w1 * modular1::mod();int n = (int)p.size() + (int)q.size() - 1;vector<T> res(n);for(auto i = 0; i < n; ++ i){using ull = unsigned long long;ull a = xy0[i].data;ull b = (xy1[i].data + modular1::mod() - a) * r01.data % modular1::mod();ull c = ((xy2[i].data + modular2::mod() - a) * r02r12.data + (modular2::mod() - b) * r12.data) % modular2::mod();res[i] = xy0[i].data + w1 * b + w2 * c;}return res;}};template<class T> vector<T> number_theoric_transform_wrapper<T>::root;template<class T> vector<T> number_theoric_transform_wrapper<T>::buffer1;template<class T> vector<T> number_theoric_transform_wrapper<T>::buffer2;using ntt = number_theoric_transform_wrapper<modular>;// T must support *=, *, +=, -=, and -// T{} should return the additive identity// Requires modular and number_theoric_transformtemplate<class T, class FFT>struct power_series_base: vector<T>{#define data (*this)template<class ...Args>power_series_base(Args... args): vector<T>(args...){}power_series_base(initializer_list<T> init): vector<T>(init){}int degree() const{return data.empty() ? numeric_limits<int>::max() : data.size() - 1;}// Returns \sum_{i=0}^{n-1} a_i/i! * X^istatic power_series_base EGF(vector<T> a){int n = (int)a.size();T fact = 1;for(auto x = 2; x < n; ++ x) fact *= x;fact = 1 / fact;for(auto i = n - 1; i >= 0; -- i) a[i] *= fact, fact *= i;return power_series_base(a);}// Returns exp(coef * X).prefix(n) = \sum_{i=0}^{n-1} coef^i/i! * X^istatic power_series_base EGF(int n, T coef = 1){vector<T> a(n, 1);for(auto i = 1; i < n; ++ i) a[i] = a[i - 1] * coef;return EGF(a);}vector<T> EGF_to_seq() const{int n = (int)data.size();vector<T> seq(n);T fact = 1;for(auto i = 0; i < n; ++ i){seq[i] = data[i] * fact;fact *= i + 1;}return seq;}power_series_base &reduce(){while(!data.empty() && !data.back()) data.pop_back();return *this;}power_series_base reduced() const{return power_series_base(*this).reduce();}friend ostream &operator<<(ostream &out, const power_series_base &p){if(p.empty()) return out << "{}";else{out << "{";for(auto i = 0; i < (int)p.size(); ++ i){out << p[i];i + 1 < (int)p.size() ? out << ", " : out << "}";}return out;}}power_series_base &inplace_take(int n){data.erase(data.begin() + min((int)data.size(), n), data.end());data.resize(n, T{});return *this;}power_series_base take(int n) const{return power_series_base(*this).inplace_take(n);}power_series_base &inplace_drop(int n){data.erase(data.begin(), data.begin() + min((int)data.size(), n));return *this;}power_series_base drop(int n) const{return power_series_base(*this).inplace_drop(n);}power_series_base &inplace_reverse(int n){data.resize(max(n, (int)data.size()));std::reverse(data.begin(), data.begin() + n);return *this;}power_series_base reverse(int n) const{return power_series_base(*this).inplace_reverse(n);}T evaluate(T x) const{T res = {};for(auto i = (int)data.size() - 1; i >= 0; -- i) res = res * x + data[i];return res;}power_series_base operator*(const power_series_base &p) const{return FFT::convolute(data, p);}power_series_base &operator*=(const power_series_base &p){return *this = *this * p;}template<class U>power_series_base &operator*=(U x){for(auto &c: data) c *= x;return *this;}template<class U>power_series_base operator*(U x) const{return power_series_base(*this) *= x;}template<class U>friend power_series_base operator*(U x, power_series_base p){for(auto &c: p) c = x * c;return p;}power_series_base &operator+=(const power_series_base &p){data.resize(max(data.size(), p.size()));for(auto i = 0; i < (int)p.size(); ++ i) data[i] += p[i];return *this;}power_series_base operator+(const power_series_base &p) const{return power_series_base(*this) += p;}template<class U>power_series_base &operator+=(const U &x){if(data.empty()) data.emplace_back();data[0] += x;return *this;}template<class U>power_series_base operator+(const U &x) const{return power_series_base(*this) += x;}template<class U>friend power_series_base operator+(const U &x, const power_series_base &p){return p + x;}power_series_base &operator-=(const power_series_base &p){data.resize(max(data.size(), p.size()));for(auto i = 0; i < (int)p.size(); ++ i) data[i] -= p[i];return *this;}power_series_base operator-(const power_series_base &p) const{return power_series_base(*this) -= p;}template<class U>power_series_base &operator-=(const U &x){if(data.empty()) data.emplace_back();data[0] -= x;return *this;}template<class U>power_series_base operator-(const U &x) const{return power_series_base(*this) -= x;}template<class U>friend power_series_base operator-(const U &x, const power_series_base &p){return -p + x;}power_series_base operator-() const{power_series_base res = *this;for(auto i = 0; i < data.size(); ++ i) res[i] = T{} - res[i];return res;}power_series_base &operator++(){if(data.empty()) data.push_back(1);else ++ data[0];return *this;}power_series_base &operator--(){if(data.empty()) data.push_back(-1);else -- data[0];return *this;}power_series_base operator++(int){power_series_base result(*this);if(data.empty()) data.push_back(1);else ++ data[0];return result;}power_series_base operator--(int){power_series_base result(*this);if(data.empty()) data.push_back(-1);else -- data[0];return result;}power_series_base &clear_range(int l, int r){assert(0 <= l && l <= r && r <= data.size());for(auto i = l; i < r; ++ i) data[i] = 0;return *this;}power_series_base &transform(bool invert = false){FFT::transform(data, invert);return *this;}power_series_base transformed(bool invert = false) const{auto res = *this;res.transform(invert);return res;}power_series_base &inplace_dot_product(const power_series_base &p){for(auto i = 0; i < min(data.size(), p.size()); ++ i) data[i] *= p[i];return *this;}power_series_base dot_product(const power_series_base &p) const{return power_series_base(*this).inplace_power_series_product(p);}power_series_base &inverse_doubled_up(power_series_base &f, const power_series_base &freq) const{assert((f.size() & -f.size()) == f.size());int s = f.size();power_series_base buffer = take(s << 1);buffer.transform();buffer.inplace_dot_product(freq);buffer.transform(true);buffer.clear_range(0, s);buffer.transform();buffer.inplace_dot_product(freq);buffer.transform(true);f.resize(s << 1);return f -= buffer.clear_range(0, s);}power_series_base &inverse_doubled_up(power_series_base &f) const{assert((f.size() & -f.size()) == f.size());return inverse_doubled_up(f, f.take(f.size() << 1).transformed());}// Returns the first n terms of the inverse series// O(n * log(n))power_series_base inverse(int n) const{assert(!data.empty() && data[0]);auto inv = 1 / data[0];power_series_base res{inv};for(auto s = 1; s < n; s <<= 1) inverse_doubled_up(res);res.resize(n);return res;}// Returns the first n terms of the inverse series// O(n * log(n))power_series_base &inplace_inverse(int n){return *this = this->inverse(n);}// O(n * log(n))power_series_base &inplace_power_series_division(power_series_base p, int n){int i = 0;while(i < min(data.size(), p.size()) && !data[i] && !p[i]) ++ i;data.erase(data.begin(), data.begin() + i);p.erase(p.begin(), p.begin() + i);(*this *= p.inverse(n)).resize(n);return *this;}// O(n * log(n))power_series_base power_series_division(const power_series_base &p, int n){return power_series_base(*this).inplace_power_series_division(p, n);}// Euclidean division// O(n * log(n))power_series_base &operator/=(const power_series_base &p){assert(!p.empty() && p.back() != T{0});reduce();if(data.size() < p.size()){data.clear();return *this;}if((int)p.size() - count(p.begin(), p.end(), 0) <= 100){T inv = 1 / p.back();static vector<int> indices;for(auto i = 0; i < (int)p.size() - 1; ++ i) if(p[i]) indices.push_back(i);power_series_base res((int)data.size() - (int)p.size() + 1);for(auto i = (int)data.size() - 1; i >= (int)p.size() - 1; -- i) if(data[i]){T x = data[i] * inv;res[i - (int)p.size() + 1] = x;for(auto j: indices) data[i - ((int)p.size() - 1 - j)] -= x * p[j];}indices.clear();return *this = res;}power_series_base b;int n = data.size() - p.size() + 1;b.assign(n, {});copy(p.rbegin(), p.rbegin() + min(p.size(), b.size()), b.begin());std::reverse(data.begin(), data.end());data = FFT::convolute(data, b.inverse(n));data.erase(data.begin() + n, data.end());std::reverse(data.begin(), data.end());return *this;}power_series_base operator/(const power_series_base &p) const{return power_series_base(*this) /= p;}template<class U>power_series_base &operator/=(U x){assert(x);T inv_x = T(1) / x;for(auto &c: data) c *= inv_x;return *this;}template<class U>power_series_base operator/(U x) const{return power_series_base(*this) /= x;}pair<power_series_base, power_series_base> divrem(const power_series_base &p) const{auto q = *this / p, r = *this - q * p;while(!r.empty() && r.back() == 0) r.pop_back();return {q, r};}power_series_base &operator%=(const power_series_base &p){assert(!p.empty() && p.back() != T{0});reduce();if(data.size() < p.size()) return *this;if((int)p.size() - count(p.begin(), p.end(), 0) <= 100){T inv = 1 / p.back();static vector<int> indices;for(auto i = 0; i < (int)p.size() - 1; ++ i) if(p[i]) indices.push_back(i);for(auto i = (int)data.size() - 1; i >= (int)p.size() - 1; -- i) if(data[i]){T x = data[i] * inv;data[i] = 0;for(auto j: indices) data[i - ((int)p.size() - 1 - j)] -= x * p[j];}indices.clear();return reduce();}return *this = this->divrem(p).second;}power_series_base operator%(const power_series_base &p) const{return power_series_base(*this) %= p;}power_series_base &inplace_derivative(){if(!data.empty()){for(auto i = 0; i < data.size(); ++ i) data[i] *= i;data.erase(data.begin());}return *this;}// p'power_series_base derivative() const{return power_series_base(*this).inplace_derivative();}power_series_base &inplace_derivative_shift(){for(auto i = 0; i < data.size(); ++ i) data[i] *= i;return *this;}// xP'power_series_base derivative_shift() const{return power_series_base(*this).inplace_derivative_shift();}power_series_base &inplace_antiderivative(){T::precalc_inverse(data.size());data.push_back(0);for(auto i = (int)data.size() - 1; i >= 1; -- i) data[i] = data[i - 1] / i;data[0] = 0;return *this;}// Integral(P)power_series_base antiderivative() const{return power_series_base(*this).inplace_antiderivative();}power_series_base &inplace_shifted_antiderivative(){T::precalc_inverse(data.size());if(!data.empty()) data[0] = 0;for(auto i = 1; i < data.size(); ++ i) data[i] /= i;return *this;}// Integral(P/x)power_series_base shifted_antiderivative() const{return power_series_base(*this).inplace_shifted_antiderivative();}// O(n * log(n))power_series_base &inplace_log(int n){assert(!data.empty() && data[0] == 1);if(!n){data.clear();return *this;}(*this = derivative() * inverse(n)).resize(n - 1);inplace_antiderivative();return *this;}// O(n * log(n))power_series_base log(int n) const{return power_series_base(*this).inplace_log(n);}// O(n * log(n))power_series_base exp(int n) const{assert(data.empty() || data[0] == 0);power_series_base f{1}, g{1};for(auto s = 1; s < n; s <<= 1){power_series_base f2 = f.take(s << 1).transform();power_series_base g2 = g.take(s << 1).transform();power_series_base dt = take(s).inplace_derivative_shift();power_series_base w = dt;w.transform();for(auto i = 0; i < s; ++ i) w[i] *= f2[i << 1];w.transform(true);w -= f.derivative_shift();w.resize(s << 1);w.transform();w.inplace_dot_product(g2);w.transform(true);w.resize(s);w.insert(w.begin(), s, 0);w -= dt;power_series_base z = take(s << 1);z += w.inplace_shifted_antiderivative();z.transform();z.inplace_dot_product(f2);z.transform(true);f.resize(s << 1);f += z.clear_range(0, s);if(s << 1 < n) f.inverse_doubled_up(g, g2);}f.resize(n);return f;}// O(n * log(n))power_series_base &inplace_exp(int n){return *this = this->exp(n);}// O(n * log(n))template<class U>power_series_base &inplace_power(U e, int n){data.resize(n);if(e == 0 || n == 0){if(n) data[0] = 1;return *this;}if(e < 0) return inplace_inverse(n).inplace_power(-e, n);if(all_of(data.begin(), data.end(), [&](auto x){ return x == 0; })) return *this;int pivot = find_if(data.begin(), data.end(), [&](auto x){ return x; }) - data.begin();if(pivot && e >= (n + pivot - 1) / pivot){fill(data.begin(), data.end(), 0);return *this;}data.erase(data.begin(), data.begin() + pivot);n -= pivot * e;T pivot_c = data[0].power(e);((*this /= data[0]).inplace_log(n) *= e).inplace_exp(n);data.insert(data.begin(), pivot * e, 0);return *this *= pivot_c;}// O(n * log(n))template<class U>power_series_base power(U e, int n) const{return power_series_base(*this).inplace_power(e, n);}static power_series_base multiply_all(const vector<power_series_base> &a){if(a.empty()) return {1};auto solve = [&](auto self, int l, int r)->power_series_base{if(r - l == 1) return a[l];int m = l + (r - l >> 1);return self(self, l, m) * self(self, m, r);};return solve(solve, 0, (int)a.size());}#undef data};using power_series = power_series_base<modular, ntt>;int main(){cin.tie(0)->sync_with_stdio(0);cin.exceptions(ios::badbit | ios::failbit);int nr, nc, n, k;cin >> nr >> nc >> n >> k;combinatorics<modular> C(n);if(nr > nc){swap(nr, nc);}auto inv = modular(1) / (nr - (k - 1)) / (nc - (k - 1));auto invpower = modular::precalc_power(inv, n);auto kpower = modular::precalc_power(k, n << 1);modular res = 0;if(2 * k <= nr){auto sum = ((1 - power_series::EGF(n + 2, k + 1)).drop(1) * (1 - power_series::EGF(n + 2)).drop(1).inverse(n + 1)).EGF_to_seq();for(auto i = 1; i <= n; ++ i){res += C.C(n, i) * invpower[i] * modular(-1).power(i - 1) * sum[i] * sum[i] * 4;}for(auto i = 1; i <= n; ++ i){res += C.C(n, i) * invpower[i] * modular(-1).power(i - 1) * sum[i] * kpower[i] * 2 * (nr + nc - 4 * k);}for(auto i = 1; i <= n; ++ i){res += C.C(n, i) * invpower[i] * modular(-1).power(i - 1) * kpower[i << 1] * (nr - 2 * k) * (nc - 2 * k);}}else if(2 * k <= nc){}else{}cout << res << "\n";return 0;}/**/////////////////////////////////////////////////////////////////////////////////////////// //// Coded by Aeren //// //////////////////////////////////////////////////////////////////////////////////////////