結果
問題 | No.1856 Mex Sum 2 |
ユーザー | tamato |
提出日時 | 2022-02-26 11:13:02 |
言語 | PyPy3 (7.3.15) |
結果 |
TLE
|
実行時間 | - |
コード長 | 3,911 bytes |
コンパイル時間 | 593 ms |
コンパイル使用メモリ | 87,140 KB |
実行使用メモリ | 140,484 KB |
最終ジャッジ日時 | 2023-09-17 10:31:09 |
合計ジャッジ時間 | 19,090 ms |
ジャッジサーバーID (参考情報) |
judge12 / judge11 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 79 ms
80,144 KB |
testcase_01 | AC | 78 ms
75,816 KB |
testcase_02 | AC | 121 ms
77,144 KB |
testcase_03 | AC | 79 ms
75,756 KB |
testcase_04 | AC | 96 ms
76,868 KB |
testcase_05 | AC | 83 ms
76,408 KB |
testcase_06 | AC | 83 ms
76,456 KB |
testcase_07 | AC | 88 ms
76,312 KB |
testcase_08 | AC | 79 ms
75,892 KB |
testcase_09 | AC | 83 ms
76,236 KB |
testcase_10 | AC | 81 ms
76,532 KB |
testcase_11 | AC | 83 ms
76,236 KB |
testcase_12 | AC | 81 ms
75,656 KB |
testcase_13 | AC | 79 ms
75,884 KB |
testcase_14 | AC | 79 ms
75,756 KB |
testcase_15 | AC | 79 ms
75,916 KB |
testcase_16 | AC | 85 ms
76,220 KB |
testcase_17 | AC | 118 ms
77,396 KB |
testcase_18 | AC | 112 ms
77,200 KB |
testcase_19 | AC | 83 ms
76,296 KB |
testcase_20 | AC | 85 ms
76,204 KB |
testcase_21 | AC | 81 ms
75,960 KB |
testcase_22 | AC | 118 ms
76,880 KB |
testcase_23 | AC | 80 ms
75,908 KB |
testcase_24 | AC | 89 ms
76,572 KB |
testcase_25 | AC | 114 ms
77,392 KB |
testcase_26 | AC | 80 ms
75,736 KB |
testcase_27 | AC | 77 ms
75,640 KB |
testcase_28 | AC | 80 ms
75,984 KB |
testcase_29 | AC | 1,141 ms
90,500 KB |
testcase_30 | AC | 643 ms
84,196 KB |
testcase_31 | AC | 1,100 ms
89,936 KB |
testcase_32 | AC | 1,630 ms
97,360 KB |
testcase_33 | AC | 1,810 ms
99,648 KB |
testcase_34 | AC | 1,102 ms
89,496 KB |
testcase_35 | AC | 659 ms
84,236 KB |
testcase_36 | AC | 346 ms
80,752 KB |
testcase_37 | AC | 1,068 ms
89,540 KB |
testcase_38 | AC | 278 ms
79,456 KB |
testcase_39 | AC | 101 ms
77,052 KB |
testcase_40 | AC | 115 ms
77,360 KB |
testcase_41 | AC | 116 ms
77,352 KB |
testcase_42 | TLE | - |
testcase_43 | -- | - |
testcase_44 | -- | - |
testcase_45 | -- | - |
testcase_46 | -- | - |
testcase_47 | -- | - |
testcase_48 | -- | - |
testcase_49 | -- | - |
testcase_50 | -- | - |
testcase_51 | -- | - |
testcase_52 | -- | - |
testcase_53 | -- | - |
testcase_54 | -- | - |
testcase_55 | -- | - |
testcase_56 | -- | - |
testcase_57 | -- | - |
testcase_58 | -- | - |
testcase_59 | -- | - |
testcase_60 | -- | - |
testcase_61 | -- | - |
testcase_62 | -- | - |
testcase_63 | -- | - |
testcase_64 | -- | - |
testcase_65 | -- | - |
testcase_66 | -- | - |
ソースコード
mod = 998244353 W = ( 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) def main(): import sys input = sys.stdin.readline # A: 係数を並べたベクトル,len(A) = 2^n def fft(A): N = len(A) n = N.bit_length() - 1 N2 = N // 2 A_new = [0] * N for lv in range(n): L = 1 << (n - lv - 1) w = W[lv + 1] ww = 1 for 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) % mod A_new[i + j * L] = (f0_val + tmp) % mod A_new[i + j * L + N2] = (f0_val - tmp) % mod ww = (ww * w) % mod A, A_new = A_new, A return A # A: 係数を並べたベクトル,len(A) = 2^n def ifft(A): N = len(A) n = N.bit_length() - 1 N2 = N // 2 A_new = [0] * N for lv in range(n): L = 1 << (n - lv - 1) w = IW[lv + 1] ww = 1 for 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) % mod A_new[i + j * L] = (f0_val + tmp) % mod A_new[i + j * L + N2] = (f0_val - tmp) % mod ww = (ww * w) % mod A, A_new = A_new, A return A def convolution(A0, B0, limit): if len(A0) <= 60 or len(B0) <= 60: return convolution_naive(A0, B0, limit) N = len(A0) + len(B0) - 1 N0 = 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) % mod return C[:limit] # comb init nmax = 2 * 10 ** 3 + 10 # change here fac = [0] * nmax finv = [0] * nmax inv = [0] * nmax fac[0] = 1 fac[1] = 1 finv[0] = 1 finv[1] = 1 inv[1] = 1 for i in range(2, nmax): fac[i] = fac[i - 1] * i % mod inv[i] = mod - inv[mod % i] * (mod // i) % mod finv[i] = finv[i - 1] * inv[i] % mod def comb(n, r): if n < r: return 0 else: return (fac[n] * ((finv[r] * finv[n - r]) % mod)) % mod N, 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)) ans = 0 for i in range(min(N, M + 1)): for j in range(N + 1): if i == M: if j == N: ans = (ans + dp[i][j])%mod else: ans = (ans + ((dp[i][j] * pow(M - i, N - j, mod))%mod * (finv[N - j] * pow(2, N - j, mod))%mod)%mod)%mod print((ans * fac[N])%mod) if __name__ == '__main__': main()