結果

問題 No.1856 Mex Sum 2
ユーザー MitarushiMitarushi
提出日時 2021-04-17 17:48:26
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,350 ms / 3,000 ms
コード長 1,789 bytes
コンパイル時間 403 ms
コンパイル使用メモリ 81,844 KB
実行使用メモリ 77,632 KB
最終ジャッジ日時 2024-07-04 04:43:53
合計ジャッジ時間 40,095 ms
ジャッジサーバーID
(参考情報)
judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 64
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 fft_inplace(a, w):
n = len(a)
m = n
t = 1
while m >= 2:
mh = m >> 1
for i in range(0, n, m):
for s in range(mh):
j, k = i+s, i+mh+s
a[j], a[k] = a[j]+a[k], (a[j]-a[k])*w[s*t] % mod
m = mh
t *= 2
def ifft_inplace(a, w):
n = len(a)
m = 2
t = -(n >> 1)
while m <= n:
mh = m >> 1
for i in range(0, n, m):
for s in range(mh):
j, k = i+s, i+mh+s
a[k] = a[k] * w[s*t] % mod
a[j], a[k] = a[j]+a[k], a[j]-a[k]
m <<= 1
t //= 2
n_inv = pow(n, mod-2, mod)
for i in range(n):
a[i] = a[i] * n_inv % mod
n, m = map(int, input().split())
fixed_n = 1 << ((n+1)*2).bit_length()
w_root = pow(3, (mod-1)//fixed_n, mod)
w = [1] * fixed_n
for i in range(1, fixed_n):
w[i] = w[i-1] * w_root % mod
frac = [1] * (n + 1)
for i in range(1, n+1):
frac[i] = frac[i-1] * i % mod
frac_inv = [0] * (n+1)
frac_inv[n] = pow(frac[n], mod-2, mod)
for i in range(1, n+1)[::-1]:
frac_inv[i-1] = frac_inv[i] * i % mod
dp1 = [0] * fixed_n
dp1[0] = 1
t = [0] * fixed_n
for i in range(n+1):
t[i] = (pow(2, i, mod)-1) * pow(pow(2, i, mod) * frac[i], mod-2, mod) % mod
fft_inplace(t, w)
ans_sub = [0] * (n+1)
for k in range(min(n, m+1)):
fft_inplace(dp1, w)
for i, j in enumerate(t):
dp1[i] = dp1[i] * j % mod
ifft_inplace(dp1, w)
pow_tmp = 1
for i in range(k+1, n+1)[::-1]:
ans_sub[i] += dp1[i] * pow_tmp % mod
pow_tmp = pow_tmp * (m - k) % mod
for i in range(n+1, fixed_n):
dp1[i] = 0
ans = sum(ans_sub[i] % mod * frac_inv[n-i] for i in range(n+1)) % mod
ans = ans * pow(2, n, mod) * frac[n] % mod
print(ans)
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