結果
問題 | No.1856 Mex Sum 2 |
ユーザー |
![]() |
提出日時 | 2022-02-26 11:38:33 |
言語 | PyPy3 (7.3.15) |
結果 |
TLE
(最新)
AC
(最初)
|
実行時間 | - |
コード長 | 4,050 bytes |
コンパイル時間 | 179 ms |
コンパイル使用メモリ | 82,696 KB |
実行使用メモリ | 137,832 KB |
最終ジャッジ日時 | 2024-12-24 02:40:19 |
合計ジャッジ時間 | 85,946 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 45 TLE * 19 |
ソースコード
mod = 998244353def main():import sysinput = sys.stdin.readlineW = (1, 998244352, 911660635, 372528824, 929031873, 452798380, 922799308, 781712469, 476477967, 166035806, 258648936,584193783, 63912897, 350007156, 666702199, 968855178, 629671588, 24514907, 996173970, 363395222, 565042129,733596141, 267099868, 15311432)IW = (1, 998244352, 86583718, 509520358, 337190230, 87557064, 609441965, 135236158, 304459705, 685443576, 381598368,335559352, 129292727, 358024708, 814576206, 708402881, 283043518, 3707709, 121392023, 704923114, 950391366,428961804, 382752275, 469870224)# A: 係数を並べたベクトル,len(A) = 2^ndef fft(A):N = len(A)n = N.bit_length() - 1N2 = N // 2A_new = [0] * Nfor lv in range(n):L = 1 << (n - lv - 1)w = W[lv + 1]ww = 1for j in range(1 << lv):for i in range(L):f0_val = A[i + j * L * 2]f1_val = A[i + j * L * 2 + L]tmp = (ww * f1_val) % modA_new[i + j * L] = (f0_val + tmp) % modA_new[i + j * L + N2] = (f0_val - tmp) % modww = (ww * w) % modA, A_new = A_new, Areturn A# A: 係数を並べたベクトル,len(A) = 2^ndef ifft(A):N = len(A)n = N.bit_length() - 1N2 = N // 2A_new = [0] * Nfor lv in range(n):L = 1 << (n - lv - 1)w = IW[lv + 1]ww = 1for j in range(1 << lv):for i in range(L):f0_val = A[i + j * L * 2]f1_val = A[i + j * L * 2 + L]tmp = (ww * f1_val) % modA_new[i + j * L] = (f0_val + tmp) % modA_new[i + j * L + N2] = (f0_val - tmp) % modww = (ww * w) % modA, A_new = A_new, Areturn Adef convolution(A0, B0, limit):if len(A0) <= 60 or len(B0) <= 60:return convolution_naive(A0, B0, limit)N = len(A0) + len(B0) - 1N0 = 1 << ((N - 1).bit_length())A = A0 + [0] * (N0 - len(A0))B = B0 + [0] * (N0 - len(B0))AA = fft(A)BB = fft(B)CC = [(aa * bb) % mod for aa, bb in zip(AA, BB)]C = ifft(CC)invN0 = pow(N0, mod - 2, mod)C = [(c * invN0) % mod for c in C]return C[:limit]def convolution_naive(A0, B0, limit):NA = len(A0)NB = len(B0)C = [0] * (NA + NB - 1)for i in range(NA):for j in range(NB):C[i + j] = (C[i + j] + (A0[i] * B0[j]) % mod) % modreturn C[:limit]# comb initnmax = 2 * 10 ** 3 + 10 # change herefac = [0] * nmaxfinv = [0] * nmaxinv = [0] * nmaxfac[0] = 1fac[1] = 1finv[0] = 1finv[1] = 1inv[1] = 1for i in range(2, nmax):fac[i] = fac[i - 1] * i % modinv[i] = mod - inv[mod % i] * (mod // i) % modfinv[i] = finv[i - 1] * inv[i] % moddef comb(n, r):if n < r:return 0else:return (fac[n] * ((finv[r] * finv[n - r]) % mod)) % modN, M = map(int, input().split())vec = []for i in range(N+1):vec.append(((pow(2, i, mod) - 1) * finv[i])%mod)dp = [vec[:]]for i in range(1, min(N, M + 1)):dp.append(convolution(vec, dp[-1], N+1))vec.pop()ans = 0for i in range(min(N, M + 1)):powM = 1pow2 = 1for j in range(N, -1, -1):if i == M:if j == N:ans = (ans + dp[i][j])%modelse:ans = (ans + ((dp[i][j] * powM)%mod * (finv[N - j] * pow2)%mod)%mod)%modpowM = (powM * (M - i))%modpow2 = (pow2 * 2)%modprint((ans * fac[N])%mod)if __name__ == '__main__':main()