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 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
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 45 TLE * 19
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

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: 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: 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()
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