結果
問題 | No.1856 Mex Sum 2 |
ユーザー | tamato |
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 | 445 ms |
コンパイル使用メモリ | 87,168 KB |
実行使用メモリ | 138,280 KB |
最終ジャッジ日時 | 2023-09-17 11:24:01 |
合計ジャッジ時間 | 83,122 ms |
ジャッジサーバーID (参考情報) |
judge12 / judge13 |
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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 | 75 ms
75,860 KB |
testcase_01 | AC | 78 ms
75,708 KB |
testcase_02 | AC | 117 ms
77,644 KB |
testcase_03 | AC | 76 ms
75,972 KB |
testcase_04 | AC | 92 ms
77,176 KB |
testcase_05 | AC | 77 ms
76,468 KB |
testcase_06 | AC | 79 ms
76,496 KB |
testcase_07 | AC | 86 ms
76,632 KB |
testcase_08 | AC | 74 ms
75,996 KB |
testcase_09 | AC | 82 ms
76,496 KB |
testcase_10 | AC | 81 ms
76,016 KB |
testcase_11 | AC | 80 ms
76,244 KB |
testcase_12 | AC | 78 ms
75,788 KB |
testcase_13 | AC | 77 ms
75,864 KB |
testcase_14 | AC | 74 ms
75,704 KB |
testcase_15 | AC | 75 ms
75,920 KB |
testcase_16 | AC | 80 ms
76,472 KB |
testcase_17 | AC | 106 ms
77,448 KB |
testcase_18 | AC | 96 ms
77,060 KB |
testcase_19 | AC | 79 ms
76,312 KB |
testcase_20 | AC | 82 ms
76,240 KB |
testcase_21 | AC | 76 ms
75,860 KB |
testcase_22 | AC | 110 ms
77,520 KB |
testcase_23 | AC | 77 ms
75,972 KB |
testcase_24 | AC | 86 ms
76,308 KB |
testcase_25 | AC | 108 ms
77,236 KB |
testcase_26 | AC | 77 ms
75,868 KB |
testcase_27 | AC | 75 ms
76,016 KB |
testcase_28 | AC | 77 ms
75,904 KB |
testcase_29 | AC | 761 ms
90,804 KB |
testcase_30 | AC | 448 ms
84,436 KB |
testcase_31 | AC | 732 ms
90,320 KB |
testcase_32 | AC | 1,091 ms
97,620 KB |
testcase_33 | AC | 1,138 ms
99,944 KB |
testcase_34 | AC | 735 ms
90,580 KB |
testcase_35 | AC | 478 ms
84,520 KB |
testcase_36 | AC | 259 ms
80,592 KB |
testcase_37 | AC | 705 ms
89,796 KB |
testcase_38 | AC | 212 ms
79,604 KB |
testcase_39 | AC | 98 ms
77,108 KB |
testcase_40 | AC | 109 ms
77,644 KB |
testcase_41 | AC | 110 ms
77,332 KB |
testcase_42 | AC | 2,824 ms
134,940 KB |
testcase_43 | AC | 2,361 ms
123,360 KB |
testcase_44 | AC | 2,543 ms
128,104 KB |
testcase_45 | AC | 2,796 ms
134,100 KB |
testcase_46 | AC | 2,370 ms
123,996 KB |
testcase_47 | AC | 2,594 ms
129,312 KB |
testcase_48 | AC | 2,927 ms
135,400 KB |
testcase_49 | AC | 2,846 ms
135,904 KB |
testcase_50 | AC | 2,028 ms
118,148 KB |
testcase_51 | AC | 2,987 ms
137,708 KB |
testcase_52 | AC | 2,969 ms
137,656 KB |
testcase_53 | AC | 2,980 ms
137,932 KB |
testcase_54 | AC | 2,967 ms
137,888 KB |
testcase_55 | AC | 2,976 ms
137,972 KB |
testcase_56 | AC | 2,985 ms
138,136 KB |
testcase_57 | AC | 2,970 ms
137,984 KB |
testcase_58 | AC | 2,978 ms
138,272 KB |
testcase_59 | TLE | - |
testcase_60 | AC | 2,970 ms
137,988 KB |
testcase_61 | AC | 2,973 ms
137,716 KB |
testcase_62 | AC | 2,972 ms
137,716 KB |
testcase_63 | AC | 2,956 ms
137,932 KB |
testcase_64 | AC | 2,938 ms
137,960 KB |
testcase_65 | AC | 2,965 ms
137,888 KB |
testcase_66 | AC | 2,955 ms
138,192 KB |
ソースコード
mod = 998244353 def main(): import sys input = sys.stdin.readline 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) # 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)) vec.pop() ans = 0 for i in range(min(N, M + 1)): powM = 1 pow2 = 1 for j in range(N, -1, -1): if i == M: if j == N: ans = (ans + dp[i][j])%mod else: ans = (ans + ((dp[i][j] * powM)%mod * (finv[N - j] * pow2)%mod)%mod)%mod powM = (powM * (M - i))%mod pow2 = (pow2 * 2)%mod print((ans * fac[N])%mod) if __name__ == '__main__': main()