結果
問題 | No.2459 Stampaholic (Hard) |
ユーザー |
![]() |
提出日時 | 2023-09-01 23:00:14 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,183 ms / 4,000 ms |
コード長 | 25,920 bytes |
コンパイル時間 | 4,628 ms |
コンパイル使用メモリ | 262,796 KB |
実行使用メモリ | 54,412 KB |
最終ジャッジ日時 | 2025-01-03 11:01:39 |
合計ジャッジ時間 | 18,897 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 19 |
ソースコード
#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <chrono>#include <cmath>#include <complex>#include <deque>#include <forward_list>#include <fstream>#include <functional>#include <iomanip>#include <ios>#include <iostream>#include <limits>#include <list>#include <map>#include <memory>#include <numeric>#include <optional>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <string>#include <tuple>#include <type_traits>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>using namespace std;using lint = long long;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v<< ','; os << ']'; return os; }template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);},tpl); return is; }template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) {((os << args << ','), ...);}, tpl); return os << ')'; }template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os<< v << ','; os << '}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os <<'}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v <<','; os << '}'; return os; }template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for(auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }#ifdef HITONANODE_LOCALconst string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET<< std::endl#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " <<__FILE__ << COLOR_RESET << std::endl : std::cerr)#else#define dbg(x) ((void)0)#define dbgif(cond, x) ((void)0)#endif#include <cassert>#include <iostream>#include <set>#include <vector>template <int md> struct ModInt {using lint = long long;constexpr static int mod() { return md; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&]() {std::set<int> fac;int v = md - 1;for (lint i = 2; i * i <= v; i++)while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < md; g++) {bool ok = true;for (auto i : fac)if (ModInt(g).pow((md - 1) / i) == 1) {ok = false;break;}if (ok) return g;}return -1;}();}return primitive_root;}int val_;int val() const noexcept { return val_; }constexpr ModInt() : val_(0) {}constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }constexpr ModInt(lint v) { _setval(v % md + md); }constexpr explicit operator bool() const { return val_ != 0; }constexpr ModInt operator+(const ModInt &x) const {return ModInt()._setval((lint)val_ + x.val_);}constexpr ModInt operator-(const ModInt &x) const {return ModInt()._setval((lint)val_ - x.val_ + md);}constexpr ModInt operator*(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.val_ % md);}constexpr ModInt operator/(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.inv().val() % md);}constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }friend constexpr ModInt operator+(lint a, const ModInt &x) {return ModInt()._setval(a % md + x.val_);}friend constexpr ModInt operator-(lint a, const ModInt &x) {return ModInt()._setval(a % md - x.val_ + md);}friend constexpr ModInt operator*(lint a, const ModInt &x) {return ModInt()._setval(a % md * x.val_ % md);}friend constexpr ModInt operator/(lint a, const ModInt &x) {return ModInt()._setval(a % md * x.inv().val() % md);}constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }constexpr bool operator<(const ModInt &x) const {return val_ < x.val_;} // To use std::map<ModInt, T>friend std::istream &operator>>(std::istream &is, ModInt &x) {lint t;return is >> t, x = ModInt(t), is;}constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {return os << x.val_;}constexpr ModInt pow(lint n) const {ModInt ans = 1, tmp = *this;while (n) {if (n & 1) ans *= tmp;tmp *= tmp, n >>= 1;}return ans;}static constexpr int cache_limit = std::min(md, 1 << 21);static std::vector<ModInt> facs, facinvs, invs;constexpr static void _precalculation(int N) {const int l0 = facs.size();if (N > md) N = md;if (N <= l0) return;facs.resize(N), facinvs.resize(N), invs.resize(N);for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;facinvs[N - 1] = facs.back().pow(md - 2);for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];}constexpr ModInt inv() const {if (this->val_ < cache_limit) {if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return invs[this->val_];} else {return this->pow(md - 2);}}constexpr ModInt fac() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facs[this->val_];}constexpr ModInt facinv() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facinvs[this->val_];}constexpr ModInt doublefac() const {lint k = (this->val_ + 1) / 2;return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()): ModInt(k).fac() * ModInt(2).pow(k);}constexpr ModInt nCr(int r) const {if (r < 0 or this->val_ < r) return ModInt(0);return this->fac() * (*this - r).facinv() * ModInt(r).facinv();}constexpr ModInt nPr(int r) const {if (r < 0 or this->val_ < r) return ModInt(0);return this->fac() * (*this - r).facinv();}static ModInt binom(int n, int r) {static long long bruteforce_times = 0;if (r < 0 or n < r) return ModInt(0);if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r);r = std::min(r, n - r);ModInt ret = ModInt(r).facinv();for (int i = 0; i < r; ++i) ret *= n - i;bruteforce_times += r;return ret;}// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)// Complexity: O(sum(ks))template <class Vec> static ModInt multinomial(const Vec &ks) {ModInt ret{1};int sum = 0;for (int k : ks) {assert(k >= 0);ret *= ModInt(k).facinv(), sum += k;}return ret * ModInt(sum).fac();}// Catalan number, C_n = binom(2n, n) / (n + 1)// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...// https://oeis.org/A000108// Complexity: O(n)static ModInt catalan(int n) {if (n < 0) return ModInt(0);return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv();}ModInt sqrt() const {if (val_ == 0) return 0;if (md == 2) return val_;if (pow((md - 1) / 2) != 1) return 0;ModInt b = 1;while (b.pow((md - 1) / 2) == 1) b += 1;int e = 0, m = md - 1;while (m % 2 == 0) m >>= 1, e++;ModInt x = pow((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModInt z = b.pow(m);while (y != 1) {int j = 0;ModInt t = y;while (t != 1) j++, t *= t;z = z.pow(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModInt(std::min(x.val_, md - x.val_));}};template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};using mint = ModInt<998244353>;// Integer convolution for arbitrary mod// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.// input: a (size: n), b (size: m)// return: vector (size: n + m - 1)template <typename MODINT>std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner);constexpr int nttprimes[3] = {998244353, 167772161, 469762049};// Integer FFT (Fast Fourier Transform) for ModInt class// (Also known as Number Theoretic Transform, NTT)// is_inverse: inverse transform// ** Input size must be 2^n **template <typename MODINT> void ntt(std::vector<MODINT> &a, bool is_inverse = false) {int n = a.size();if (n == 1) return;static const int mod = MODINT::mod();static const MODINT root = MODINT::get_primitive_root();assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);static std::vector<MODINT> w{1}, iw{1};for (int m = w.size(); m < n / 2; m *= 2) {MODINT dw = root.pow((mod - 1) / (4 * m)), dwinv = 1 / dw;w.resize(m * 2), iw.resize(m * 2);for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;}if (!is_inverse) {for (int m = n; m >>= 1;) {for (int s = 0, k = 0; s < n; s += 2 * m, k++) {for (int i = s; i < s + m; i++) {MODINT x = a[i], y = a[i + m] * w[k];a[i] = x + y, a[i + m] = x - y;}}}} else {for (int m = 1; m < n; m *= 2) {for (int s = 0, k = 0; s < n; s += 2 * m, k++) {for (int i = s; i < s + m; i++) {MODINT x = a[i], y = a[i + m];a[i] = x + y, a[i + m] = (x - y) * iw[k];}}}int n_inv = MODINT(n).inv().val();for (auto &v : a) v *= n_inv;}}template <int MOD>std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {int sz = a.size();assert(a.size() == b.size() and __builtin_popcount(sz) == 1);std::vector<ModInt<MOD>> ap(sz), bp(sz);for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];ntt(ap, false);if (a == b)bp = ap;elsentt(bp, false);for (int i = 0; i < sz; i++) ap[i] *= bp[i];ntt(ap, true);return ap;}long long garner_ntt_(int r0, int r1, int r2, int mod) {using mint2 = ModInt<nttprimes[2]>;static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv().val();static const long long m01_inv_m2 = mint2(m01).inv().val();int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val()) % mod;}template <typename MODINT>std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner) {if (a.empty() or b.empty()) return {};int sz = 1, n = a.size(), m = b.size();while (sz < n + m) sz <<= 1;if (sz <= 16) {std::vector<MODINT> ret(n + m - 1);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];}return ret;}int mod = MODINT::mod();if (skip_garner orstd::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) {a.resize(sz), b.resize(sz);if (a == b) {ntt(a, false);b = a;} else {ntt(a, false), ntt(b, false);}for (int i = 0; i < sz; i++) a[i] *= b[i];ntt(a, true);a.resize(n + m - 1);} else {std::vector<int> ai(sz), bi(sz);for (int i = 0; i < n; i++) ai[i] = a[i].val();for (int i = 0; i < m; i++) bi[i] = b[i].val();auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);a.resize(n + m - 1);for (int i = 0; i < n + m - 1; i++)a[i] = garner_ntt_(ntt0[i].val(), ntt1[i].val(), ntt2[i].val(), mod);}return a;}template <typename MODINT>std::vector<MODINT> nttconv(const std::vector<MODINT> &a, const std::vector<MODINT> &b) {return nttconv<MODINT>(a, b, false);}namespace fps_nttmod {// Calculate the inverse of f(x) mod x^d// f(x) * g(x) = 1 mod x^d// If d = -1, d is set to f.size()// Complexity: O(d log d)template <class NTTModInt> std::vector<NTTModInt> inv(const std::vector<NTTModInt> &f, int d = -1) {assert(d >= -1);const int n = f.size();if (d == -1) d = n;if (d == 0) return {};assert(f.front() != NTTModInt(0));using F = std::vector<NTTModInt>;F res{f.front().inv()}; // f(x) g_m(x) = 1 mod x^mfor (int m = 1; m < d; m *= 2) { // g_2m = (2g_m - f g_m^2) mod x^2mF g_m{res.cbegin(), res.cbegin() + m};g_m.resize(2 * m);ntt(g_m, false);F f_{f.cbegin(), f.cbegin() + std::min(n, 2 * m)};f_.resize(2 * m);ntt(f_, false);for (int i = 0; i < 2 * m; ++i) f_.at(i) *= g_m.at(i);ntt(f_, true);std::rotate(f_.begin(), f_.begin() + m, f_.end());for (int i = m; i < 2 * m; ++i) f_.at(i) = 0;ntt(f_, false);for (int i = 0; i < 2 * m; ++i) f_.at(i) *= g_m.at(i);ntt(f_, true);for (int i = 0; i < m; ++i) f_.at(i) = -f_.at(i);res.insert(res.end(), f_.begin(), f_.begin() + m);}res.resize(d);return res;}// Calculate the integral of f(x)// Complexity: O(len(f))template <class NTTModInt> void integ_inplace(std::vector<NTTModInt> &f) {if (f.empty()) return;for (int i = (int)f.size() - 1; i > 0; --i) f.at(i) = f.at(i - 1) * NTTModInt(i).inv();f.front() = NTTModInt(0);}// Calculate the derivative of f(x)// Complexity: O(len(f))template <class NTTModInt> void deriv_inplace(std::vector<NTTModInt> &f) {if (f.empty()) return;for (int i = 1; i < (int)f.size(); ++i) f.at(i - 1) = f.at(i) * i;f.back() = NTTModInt(0);}// Calculate log f(x) mod x^d// Require f(0) = 1 mod x^d// Complexity: O(d log d)template <class NTTModInt> std::vector<NTTModInt> log(const std::vector<NTTModInt> &f, int d = -1) {assert(d >= -1);const int n = f.size();if (d < 0) d = n;if (d == 0) return {};assert(f.front() == NTTModInt(1));std::vector<NTTModInt> inv_f = inv(f, d), df{f.cbegin(), f.cbegin() + std::min(d, n)};deriv_inplace(df);auto ret = nttconv(inv_f, df);ret.resize(d);integ_inplace(ret);return ret;}template <class NTTModInt> std::vector<NTTModInt> exp(const std::vector<NTTModInt> &h, int d = -1) {assert(d >= -1);const int n = h.size();if (d < 0) d = n;if (d == 0) return {};assert(h.empty() or h.front() == NTTModInt(0));using F = std::vector<NTTModInt>;F g{1}, g_fft;std::vector<NTTModInt> ret(d);ret.front() = 1;auto h_deriv = h;h_deriv.resize(d);deriv_inplace(h_deriv);for (int m = 1; m < d; m *= 2) {F f_fft = ret;f_fft.resize(m * 2);ntt(f_fft, false);// 2aif (m > 1) {F tmp{f_fft.cbegin(), f_fft.cbegin() + m};for (int i = 0; i < m; ++i) tmp.at(i) *= g_fft.at(i);ntt(tmp, true);tmp.erase(tmp.begin(), tmp.begin() + m / 2);tmp.resize(m);ntt(tmp, false);for (int i = 0; i < m; ++i) tmp.at(i) *= -g_fft.at(i);ntt(tmp, true);tmp.resize(m / 2);g.insert(g.end(), tmp.cbegin(), tmp.cbegin() + m / 2);}//F t{ret.cbegin(), ret.cbegin() + m};deriv_inplace(t);{F r{h_deriv.cbegin(), h_deriv.cbegin() + m - 1};r.resize(m);ntt(r, false);for (int i = 0; i < m; ++i) r.at(i) *= f_fft.at(i);ntt(r, true);for (int i = 0; i < m; ++i) t.at(i) -= r.at(i);std::rotate(t.begin(), t.end() - 1, t.end());}//t.resize(2 * m);ntt(t, false);g_fft = g;g_fft.resize(2 * m);ntt(g_fft, false);for (int i = 0; i < 2 * m; ++i) t.at(i) *= g_fft.at(i);ntt(t, true);t.resize(m);//F v{h.begin() + std::min(m, n), h.begin() + std::min({d, 2 * m, n})};v.resize(m);t.insert(t.begin(), m - 1, 0);t.push_back(0);integ_inplace(t);for (int i = 0; i < m; ++i) v.at(i) -= t.at(m + i);//v.resize(2 * m);ntt(v, false);for (int i = 0; i < 2 * m; ++i) v.at(i) *= f_fft.at(i);ntt(v, true);v.resize(m);for (int i = 0; i < std::min(d - m, m); ++i) ret.at(m + i) = v.at(i);}return ret;}// Calculate f(x)^k mod x^d// assume 0^0 = 1template <class NTTModInt> std::vector<NTTModInt> pow(const std::vector<NTTModInt> &A, long long k, int d = -1) {assert(d >= -1);const int n = A.size();if (d < 0) d = n;if (k == 0) {std::vector<NTTModInt> ret{NTTModInt(1)}; // assume 0^0 = 1ret.resize(d);return ret;}int l = 0;long long shift = 0;while (l < (int)A.size() and A.at(l) == NTTModInt(0) and shift < d) {++l;shift += k;}if (l == (int)A.size() or shift >= d) return std::vector<NTTModInt>(d, 0);const NTTModInt cpow = A.at(l).pow(k), cinv = A.at(l).inv();std::vector<NTTModInt> tmp{A.cbegin() + l, A.cbegin() + std::min<int>(n, d - l * k + l)};for (auto &x : tmp) x *= cinv;tmp = log(tmp, d - l * k);for (auto &x : tmp) x *= k;tmp = exp(tmp, d - l * k);for (auto &x : tmp) x *= cpow;tmp.insert(tmp.begin(), l * k, NTTModInt(0));tmp.resize(d);return tmp;}} // namespace fps_nttmod// 1 から n までの p 乗和を p <= pub までvector<mint> sum_deg(int n, int pub) {vector<mint> bernoulli(pub + 10);REP(i, bernoulli.size()) bernoulli.at(i) = mint(i).facinv();bernoulli.erase(bernoulli.begin());bernoulli = fps_nttmod::inv(bernoulli);REP(i, bernoulli.size()) bernoulli.at(i) *= mint(i).fac();bernoulli.at(1) = -bernoulli.at(1);assert(bernoulli.at(1) * 2 == 1);vector<mint> f(pub + 1);REP(k, f.size()) f.at(k) = bernoulli.at(k) * mint(k).facinv() / mint(n).pow(k);vector<mint> g(pub + 3);FOR(i, 1, g.size()) g.at(i) = mint(i).facinv();const auto h = nttconv(f, g);vector<mint> sums(pub + 1);REP(p, pub + 1) sums.at(p) = h.at(p + 1) * mint(n).pow(p + 1) * mint(p).fac();return sums;}vector<mint> gen(int H, int N, int K) {const int h = min({K, H / 2, H - K});dbg(make_tuple(H, h, N));auto h_sums = sum_deg(h, N);{const mint ainv = mint(H - K + 1).inv();dbg(ainv);mint den = 1;REP(i, h_sums.size()) {h_sums.at(i) *= den;den *= ainv;}}for (auto &x : h_sums) x *= 2;if (h * 2 < H) {dbg("A");int ilo = max(0, h - K + 1);int ihi = min(h, H - 1 - (K - 1));const mint p = mint(ihi - ilo + 1) / mint(H - K + 1);const mint weight = H - h * 2;mint ppow = 1;REP(i, h_sums.size()) {h_sums.at(i) += ppow * weight;ppow *= p;}}return h_sums;}int main() {int H, W, N, K;cin >> H >> W >> N >> K;dbg(make_tuple(H, W, N, K));auto h_sums = gen(H, N, K);auto w_sums = gen(W, N, K);dbgif(h_sums.size() <= 2, h_sums);dbgif(w_sums.size() <= 2, w_sums);mint ret = 0;FOR(d, 1, N + 1) ret += mint(N).nCr(d) * h_sums.at(d) * w_sums.at(d) * mint(-1).pow(d);cout << -ret << '\n';}