結果
問題 | No.2459 Stampaholic (Hard) |
ユーザー |
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提出日時 | 2023-09-01 22:35:15 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2,603 ms / 4,000 ms |
コード長 | 3,502 bytes |
コンパイル時間 | 4,084 ms |
コンパイル使用メモリ | 236,456 KB |
最終ジャッジ日時 | 2025-02-16 16:58:44 |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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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>#include <atcoder/convolution>using namespace std;const long long MOD = 998244353;long long modpow(long long a, long long b){long long ans = 1;while (b > 0){if (b % 2 == 1){ans *= a;ans %= MOD;}a *= a;a %= MOD;b /= 2;}return ans;}long long modinv(long long a){return modpow(a, MOD - 2);}vector<long long> inverse(vector<long long> f){int N = f.size();vector<long long> ans(1);ans[0] = 1;for (int i = 1; i < N * 2; i *= 2){vector<long long> ans2 = ans;ans2.resize(i * 4);int N2 = min(N, i * 2);vector<long long> f2(i * 4, 0);for (int j = 0; j < N2; j++){f2[j] = f[j];}ans2 = atcoder::convolution(ans2, ans2);ans2.resize(i * 2);ans2 = atcoder::convolution(ans2, f2);ans2.resize(i * 2);for (int j = 0; j < i; j++){ans2[j] = MOD - ans2[j] + ans[j] * 2;ans2[j] %= MOD;}swap(ans, ans2);}ans.resize(N);return ans;}int main(){int H, W, N, K;cin >> H >> W >> N >> K;vector<long long> inv(N + 2);inv[1] = 1;for (int i = 2; i <= N + 1; i++){inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;}vector<long long> fact(N + 2);vector<long long> finv(N + 2);fact[0] = 1;finv[0] = 1;for (int i = 1; i <= N + 1; i++){fact[i] = fact[i - 1] * i % MOD;finv[i] = finv[i - 1] * inv[i] % MOD;}vector<long long> binom(N + 1);for (int i = 0; i <= N; i++){binom[i] = fact[N] * finv[i] % MOD * finv[N - i] % MOD;}int px = min(H - K + 1, K);int py = min(W - K + 1, K);int qx = H - 2 * (px - 1);int qy = W - 2 * (py - 1);long long C = MOD - modinv(H - K + 1) * modinv(W - K + 1) % MOD;vector<long long> POW_C(N + 1);vector<long long> POW_Cpx(N + 1);vector<long long> POW_Cpy(N + 1);POW_C[0] = 1;POW_Cpx[0] = 1;POW_Cpy[0] = 1;for (int i = 0; i < N; i++){POW_C[i + 1] = POW_C[i] * C % MOD;POW_Cpx[i + 1] = POW_Cpx[i] * C % MOD * px % MOD;POW_Cpy[i + 1] = POW_Cpy[i] * C % MOD * py % MOD;}auto solve = [&](long long N, int K){vector<long long> POW_N(K + 2);POW_N[0] = 1;for (int i = 0; i < K + 1; i++){POW_N[i + 1] = POW_N[i] * N % MOD;}vector<long long> num(K + 1, 0);for (int i = 0; i <= K; i++){num[i] = POW_N[i + 1] * finv[i + 1] % MOD;}vector<long long> den(K + 1, 0);for (int i = 0; i <= K; i++){den[i] = finv[i + 1];}vector<long long> den_inv = inverse(den);vector<long long> ans = atcoder::convolution(num, den_inv);for (int i = 0; i <= K; i++){ans[i] *= fact[i];ans[i] %= MOD;}ans[0]--;return ans;};vector<long long> sum_px = solve(px, N);vector<long long> sum_py = solve(py, N);long long ans1 = 0;for (int i = 0; i <= N; i++){ans1 += POW_C[i] * binom[i] % MOD * sum_px[i] % MOD * sum_py[i] % MOD;}ans1 %= MOD;ans1 *= 4;ans1 %= MOD;long long ans2 = 0;for (int i = 0; i <= N; i++){ans2 += POW_Cpy[i] * binom[i] % MOD * sum_px[i] % MOD;}ans2 %= MOD;ans2 *= 2 * qy;ans2 %= MOD;long long ans3 = 0;for (int i = 0; i <= N; i++){ans3 += POW_Cpx[i] * binom[i] % MOD * sum_py[i] % MOD;}ans3 %= MOD;ans3 *= 2 * qx;ans3 %= MOD;long long ans4 = modpow(MOD + 1 + C * px % MOD * py % MOD, N) * qx % MOD * qy % MOD;long long ans = (ans1 + ans2 + ans3 + ans4) % MOD;cout << ((long long) H * W % MOD - ans + MOD) % MOD << endl;}