結果
問題 | No.2459 Stampaholic (Hard) |
ユーザー |
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提出日時 | 2023-09-13 06:15:48 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 651 ms / 4,000 ms |
コード長 | 32,156 bytes |
コンパイル時間 | 4,354 ms |
コンパイル使用メモリ | 247,560 KB |
最終ジャッジ日時 | 2025-02-16 22:08:29 |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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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 <bits/stdc++.h>using namespace std;typedef long long ll;template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }#define all(x) (x).begin(),(x).end()#define fi first#define se second#define mp make_pair#define si(x) int(x.size())const int mod=998244353,MAX=2000005,INF=1<<30;// FPS 全部載せ// from: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9// (based on AtCoder STL)#include <algorithm>#include <array>#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {int ceil_pow2(int n) {int x = 0;while ((1U << x) < (unsigned int)(n)) x++;return x;}int bsf(unsigned int n) {#ifdef _MSC_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __builtin_ctz(n);#endif}} // namespace internal} // namespace atcoder#include <utility>namespace atcoder {namespace internal {constexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}struct barrett {unsigned int _m;unsigned long long im;barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}unsigned int umod() const { return _m; }unsigned int mul(unsigned int a, unsigned int b) const {unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};constexpr long long pow_mod_constexpr(long long x, long long n, int m) {if (m == 1) return 0;unsigned int _m = (unsigned int)(m);unsigned long long r = 1;unsigned long long y = safe_mod(x, m);while (n) {if (n & 1) r = (r * y) % _m;y = (y * y) % _m;n >>= 1;}return r;}constexpr bool is_prime_constexpr(int n) {if (n <= 1) return false;if (n == 2 || n == 7 || n == 61) return true;if (n % 2 == 0) return false;long long d = n - 1;while (d % 2 == 0) d /= 2;for (long long a : {2, 7, 61}) {long long t = d;long long y = pow_mod_constexpr(a, t, n);while (t != n - 1 && y != 1 && y != n - 1) {y = y * y % n;t <<= 1;}if (y != n - 1 && t % 2 == 0) {return false;}}return true;}template <int n> constexpr bool is_prime = is_prime_constexpr(n);constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {a = safe_mod(a, b);if (a == 0) return {b, 0};long long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u; // |m1 * u| <= |m1| * s <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}if (m0 < 0) m0 += b / s;return {s, m0};}constexpr int primitive_root_constexpr(int m) {if (m == 2) return 1;if (m == 167772161) return 3;if (m == 469762049) return 3;if (m == 754974721) return 11;if (m == 998244353) return 3;int divs[20] = {};divs[0] = 2;int cnt = 1;int x = (m - 1) / 2;while (x % 2 == 0) x /= 2;for (int i = 3; (long long)(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 (int g = 2;; g++) {bool ok = true;for (int i = 0; i < cnt; i++) {if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {ok = false;break;}}if (ok) return g;}}template <int m> constexpr int primitive_root = primitive_root_constexpr(m);} // namespace internal} // namespace atcoder#include <cassert>#include <numeric>#include <type_traits>namespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <class T>using is_signed_int128 =typename std::conditional<std::is_same<T, __int128_t>::value ||std::is_same<T, __int128>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int128 =typename std::conditional<std::is_same<T, __uint128_t>::value ||std::is_same<T, unsigned __int128>::value,std::true_type,std::false_type>::type;template <class T>using make_unsigned_int128 =typename std::conditional<std::is_same<T, __int128_t>::value,__uint128_t,unsigned __int128>;template <class T>using is_integral = typename std::conditional<std::is_integral<T>::value ||is_signed_int128<T>::value ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_signed_int = typename std::conditional<(is_integral<T>::value &&std::is_signed<T>::value) ||is_signed_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<(is_integral<T>::value &&std::is_unsigned<T>::value) ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int128<T>::value,make_unsigned_int128<T>,typename std::conditional<std::is_signed<T>::value,std::make_unsigned<T>,std::common_type<T>>::type>::type;#elsetemplate <class T> using is_integral = typename std::is_integral<T>;template <class T>using is_signed_int =typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<is_integral<T>::value &&std::is_unsigned<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int<T>::value,std::make_unsigned<T>,std::common_type<T>>::type;#endiftemplate <class T>using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;template <class T>using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;template <class T> using to_unsigned_t = typename to_unsigned<T>::type;} // namespace internal} // namespace atcoder#include <cassert>#include <numeric>#include <type_traits>#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {struct modint_base {};struct static_modint_base : modint_base {};template <class T> using is_modint = std::is_base_of<modint_base, T>;template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;} // namespace internaltemplate <int m, std::enable_if_t<(1 <= m)>* = nullptr>struct static_modint : internal::static_modint_base {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}static_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>static_modint(T v) {long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>static_modint(T v) {_v = (unsigned int)(v % umod());}static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (unsigned int)(z % umod());return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {if (prime) {assert(_v);return pow(umod() - 2);} else {auto eg = internal::inv_gcd(_v, m);assert(eg.first == 1);return eg.second;}}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = internal::is_prime<m>;};template <int id> struct dynamic_modint : internal::modint_base {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = internal::barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>dynamic_modint(T v) {long long x = (long long)(v % (long long)(mod()));if (x < 0) x += mod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>dynamic_modint(T v) {_v = (unsigned int)(v % mod());}dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v += mod() - rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator*=(const mint& rhs) {_v = bt.mul(_v, rhs._v);return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {auto eg = internal::inv_gcd(_v, mod());assert(eg.first == 1);return eg.second;}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}private:unsigned int _v;static internal::barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;namespace internal {template <class T>using is_static_modint = std::is_base_of<internal::static_modint_base, T>;template <class T>using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;template <class> struct is_dynamic_modint : public std::false_type {};template <int id>struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};template <class T>using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;} // namespace internal} // namespace atcoder#include <cassert>#include <type_traits>#include <vector>namespace atcoder {namespace internal {template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]if (first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i < cnt2 - 2; i++) {sum_e[i] = es[i] * now;now *= ies[i];}}for (int ph = 1; ph <= h; ph++) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint now = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p] * now;a[i + offset] = l + r;a[i + offset + p] = l - r;}now *= sum_e[bsf(~(unsigned int)(s))];}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly_inv(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]if (first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i < cnt2 - 2; i++) {sum_ie[i] = ies[i] * now;now *= es[i];}}for (int ph = h; ph >= 1; ph--) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint inow = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p];a[i + offset] = l + r;a[i + offset + p] =(unsigned long long)(mint::mod() + l.val() - r.val()) *inow.val();}inow *= sum_ie[bsf(~(unsigned int)(s))];}}}} // namespace internaltemplate <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (std::min(n, m) <= 60) {if (n < m) {std::swap(n, m);std::swap(a, b);}std::vector<mint> ans(n + m - 1);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {ans[i + j] += a[i] * b[j];}}return ans;}int z = 1 << internal::ceil_pow2(n + m - 1);a.resize(z);internal::butterfly(a);b.resize(z);internal::butterfly(b);for (int i = 0; i < z; i++) {a[i] *= b[i];}internal::butterfly_inv(a);a.resize(n + m - 1);mint iz = mint(z).inv();for (int i = 0; i < n + m - 1; i++) a[i] *= iz;return a;}template <unsigned int mod = 998244353,class T,std::enable_if_t<internal::is_integral<T>::value>* = nullptr>std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};using mint = static_modint<mod>;std::vector<mint> a2(n), b2(m);for (int i = 0; i < n; i++) {a2[i] = mint(a[i]);}for (int i = 0; i < m; i++) {b2[i] = mint(b[i]);}auto c2 = convolution(move(a2), move(b2));std::vector<T> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {c[i] = c2[i].val();}return c;}std::vector<long long> convolution_ll(const std::vector<long long>& a,const std::vector<long long>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};static constexpr unsigned long long MOD1 = 754974721; // 2^24static constexpr unsigned long long MOD2 = 167772161; // 2^25static constexpr unsigned long long MOD3 = 469762049; // 2^26static constexpr unsigned long long M2M3 = MOD2 * MOD3;static constexpr unsigned long long M1M3 = MOD1 * MOD3;static constexpr unsigned long long M1M2 = MOD1 * MOD2;static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;static constexpr unsigned long long i1 =internal::inv_gcd(MOD2 * MOD3, MOD1).second;static constexpr unsigned long long i2 =internal::inv_gcd(MOD1 * MOD3, MOD2).second;static constexpr unsigned long long i3 =internal::inv_gcd(MOD1 * MOD2, MOD3).second;auto c1 = convolution<MOD1>(a, b);auto c2 = convolution<MOD2>(a, b);auto c3 = convolution<MOD3>(a, b);std::vector<long long> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {unsigned long long x = 0;x += (c1[i] * i1) % MOD1 * M2M3;x += (c2[i] * i2) % MOD2 * M1M3;x += (c3[i] * i3) % MOD3 * M1M2;long long diff =c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));if (diff < 0) diff += MOD1;static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};x -= offset[diff % 5];c[i] = x;}return c;}} // namespace atcoderusing mint=atcoder::modint998244353;vector<mint> prebat(vector<mint> S,int szsum){int z = 1 << atcoder::internal::ceil_pow2(szsum-1);auto res=S;res.resize(z);atcoder::internal::butterfly(res);return res;}// szsum = aの配列の長さ + bの配列の長さvector<mint> sufbat(vector<mint> S,int szsum){int z = 1 << atcoder::internal::ceil_pow2(szsum-1);auto res=S;atcoder::internal::butterfly_inv(res);res.resize(szsum-1);mint iz = mint(z).inv();for (int i = 0; i < szsum - 1; i++) res[i] *= iz;return res;}// szsum = aの配列の長さ + bの配列の長さmint inv[MAX],fac[MAX],finv[MAX];void make(){fac[0]=fac[1]=1;finv[0]=finv[1]=1;inv[1]=1;for(int i=2;i<MAX;i++){inv[i]=-inv[mod%i]*(mod/i);fac[i]=fac[i-1]*i;finv[i]=finv[i-1]*inv[i];}}mint comb(ll a,ll b){if(a<b) return 0;return fac[a]*finv[b]*finv[a-b];}mint perm(ll a,ll b){if(a<b) return 0;return fac[a]*finv[a-b];}vector<mint> bibun(vector<mint> F,int deg){vector<mint> res(deg+1);for(int i=1;i<si(F)&&i-1<=deg;i++){res[i-1]=F[i]*i;}return res;}vector<mint> sekibun(vector<mint> F,int deg){vector<mint> res(deg+1);for(int i=0;i<min(si(F),deg);i++){res[i+1]=F[i]*inv[i+1];}return res;}vector<mint> invv(vector<mint> F,int deg){assert(F[0]!=0);mint kake=mint(F[0]).inv();for(int i=0;i<si(F);i++){F[i]*=kake;}vector<mint> G(1,1);int len=1;while(len<=deg){vector<mint> f=F;f.resize(len*2);vector<mint> g=G;g.resize(len*2);atcoder::internal::butterfly(f);atcoder::internal::butterfly(g);for(int i=0;i<len*2;i++) f[i]*=g[i];atcoder::internal::butterfly_inv(f);vector<mint> nf(len*2);for(int i=len;i<2*len;i++) nf[i-len]=f[i];f=nf;atcoder::internal::butterfly(f);for(int i=0;i<len*2;i++) f[i]*=g[i];atcoder::internal::butterfly_inv(f);mint iz=mint(len*2).inv();mint coe=-iz*iz;G.resize(len*2);for(int i=0;i<len;i++) G[len+i]=f[i]*coe;len*=2;}G.resize(deg+1);for(int i=0;i<=deg;i++) G[i]*=kake;return G;}//1/Tのdeg次以下を返すvector<mint> logg(vector<mint> F,int deg){assert(F[0]==1);vector<mint> FF=bibun(F,deg);vector<mint> waru=invv(F,deg);vector<mint> G=atcoder::convolution(FF,waru);G=sekibun(G,deg);return G;}// F0 = 1vector<mint> expp(vector<mint> F,int deg){if(si(F)){assert(F[0]==0);}vector<mint> G(1,1);int len=1;while(len<=deg){vector<mint> nex=logg(G,len*2-1);for(int i=0;i<si(nex);i++) nex[i]*=(-1);for(int i=0;i<si(nex);i++){if(i<si(F)) nex[i]+=F[i];}nex[0]++;nex=atcoder::convolution(nex,G);nex.resize(len*2);len*=2;G=nex;}G.resize(deg+1);return G;}// F0 = 0vector<mint> poww(vector<mint> F,int deg,ll K){if(K==0){vector<mint> res(deg+1);res[0]=1;return res;}if(si(F)==0){vector<mint> res(deg+1);return res;}ll geta=-1;mint kake=0;for(int i=0;i<si(F);i++){if(F[i]!=0){geta=i;kake=F[i].inv();break;}}if(geta==-1){vector<mint> res(deg+1);return res;}if(geta>1000000000LL/K){vector<mint> res(deg+1);return res;}if(geta*K>deg){vector<mint> res(deg+1);return res;}vector<mint> nF(si(F)-geta);for(int i=geta;i<si(F);i++){nF[i-geta]=(F[i]*kake);}F=nF;vector<mint> FF=logg(nF,deg-geta*K);for(int i=0;i<si(FF);i++) FF[i]*=K;vector<mint> G=expp(FF,deg-geta*K);kake=kake.inv();kake=kake.pow(K);vector<mint> res(deg+1);for(int i=0;i<si(G);i++){res[geta*K+i]=G[i]*kake;}return res;}mint senkeizenka(vector<mint> A,vector<mint> C,ll K){if(K<si(A)) return A[K];int D=si(A);assert(si(A)==si(C));vector<mint> Q(D+1);Q[0]=1;for(int i=1;i<=D;i++) Q[i]=-C[i-1];auto P=atcoder::convolution(A,Q);P.resize(D);while(K){auto Qneg=Q;for(int i=1;i<si(Qneg);i+=2) Qneg[i]=-Qneg[i];auto x=atcoder::convolution(P,Qneg);auto y=atcoder::convolution(Q,Qneg);P.clear();Q.clear();for(int i=(K&1);i<si(x);i+=2) P.push_back(x[i]);for(int i=0;i<si(y);i+=2) Q.push_back(y[i]);K/=2;}return P[0]/Q[0];}//a[0],...,a[d-1]//c[1],...,c[d]mint senkeizenka2(vector<mint> P,vector<mint> Q,ll K){while(K){auto Qneg=Q;for(int i=1;i<si(Qneg);i+=2) Qneg[i]=-Qneg[i];auto x=atcoder::convolution(P,Qneg);auto y=atcoder::convolution(Q,Qneg);P.clear();Q.clear();for(int i=(K&1);i<si(x);i+=2) P.push_back(x[i]);for(int i=0;i<si(y);i+=2) Q.push_back(y[i]);K/=2;}return P[0]/Q[0];}// P/Q// make() を呼ばないとsekibun呼ぶやつで一部バグる// MAX=2*deg ぐらい必要な気がするpair<vector<mint>,vector<mint>> warizan(vector<mint> P,vector<mint> Q){if(si(P)<si(Q)) return mp(vector<mint>{},P);auto revP=P;reverse(all(revP));auto revQ=Q;reverse(all(revQ));revQ=invv(revQ,si(P)-si(Q));auto shou=atcoder::convolution(revP,revQ);shou.resize(si(P)-si(Q)+1);reverse(all(shou));auto hiku=atcoder::convolution(Q,shou);vector<mint> amari(si(P));for(int i=0;i<si(P);i++){amari[i]=P[i]-hiku[i];}while(si(shou)&&shou.back()==0) shou.pop_back();while(si(amari)&&amari.back()==0) amari.pop_back();return mp(shou,amari);}// 最高位が0でないようにしている(0のときは空)// 多項式での除算vector<mint> multieval(vector<mint> P,vector<mint> que){if(si(que)==0) return {};int N=si(que),n=1;while(n<N) n*=2;que.resize(n);vector<vector<mint>> Atree(n+n-1),Btree(n+n-1);for(int i=0;i<n;i++) Atree[n-1+i]={-que[i],1};for(int i=n-2;i>=0;i--){Atree[i]=atcoder::convolution(Atree[2*i+1],Atree[2*i+2]);}Btree[0]=warizan(P,Atree[0]).se;for(int i=1;i<n+n-1;i++){Btree[i]=warizan(Btree[(i-1)/2],Atree[i]).se;}vector<mint> res(N,0);for(int i=0;i<N;i++){if(si(Btree[n-1+i])) res[i]=Btree[n-1+i][0];}return res;}int main(){std::ifstream in("text.txt");std::cin.rdbuf(in.rdbuf());cin.tie(0);ios::sync_with_stdio(false);make();ll H,W,N,K;cin>>H>>W>>N>>K;mint al=(H-K+1)*(W-K+1);mint ans=H*W;ll th,tw,cnh,cnw;if(H<2*K){th=H-K;}else{th=K-1;}if(W<2*K){tw=W-K;}else{tw=K-1;}cnh=H-2*th;cnw=W-2*tw;vector<mint> keiH(N+1),keiW(N+1);vector<mint> B(N+2);{vector<mint> A(N+2);for(int i=0;i<=N+1;i++){A[i]=mint(th+1).pow(i)*finv[i];B[i]=finv[i];}A.erase(A.begin());B.erase(B.begin());B=invv(B,N);auto C=atcoder::convolution(A,B);C[0]--;for(int k=0;k<=N;k++){keiH[k]=C[k]*fac[k]*2+mint(th+1).pow(k)*cnh;}}{vector<mint> A(N+2);for(int i=0;i<=N+1;i++){A[i]=mint(tw+1).pow(i)*finv[i];}A.erase(A.begin());auto C=atcoder::convolution(A,B);C[0]--;for(int k=0;k<=N;k++){keiW[k]=C[k]*fac[k]*2+mint(tw+1).pow(k)*cnw;}}al=al.inv();for(int k=0;k<=N;k++){if(k&1) ans+=comb(N,k)*al.pow(k)*keiH[k]*keiW[k];else ans-=comb(N,k)*al.pow(k)*keiH[k]*keiW[k];//cout<<keiH[k].val()<<endl;}cout<<ans.val()<<endl;}