結果

問題 No.1857 Gacha Addiction
ユーザー MitarushiMitarushi
提出日時 2021-12-31 22:58:49
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 5,181 ms / 6,000 ms
コード長 3,101 bytes
コンパイル時間 168 ms
コンパイル使用メモリ 81,520 KB
実行使用メモリ 299,692 KB
最終ジャッジ日時 2024-07-01 22:05:19
合計ジャッジ時間 116,107 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
(要ログイン)
ファイルパターン 結果
sample AC * 4
other AC * 43
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

import collections
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]) % mod, (a[j]-a[k])*w[s*t] % mod
m = mh
t <<= 1
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] *= w[s*t]
a[j], a[k] = (a[j]+a[k]) % mod, (a[j]-a[k]) % mod
m <<= 1
t //= 2
n_inv = pow(n, mod-2, mod)
for i in range(n):
a[i] = a[i] * n_inv % mod
def zero_pad(a, n):
a.extend([0] * (n - len(a)))
def zero_remove(a, n):
for _ in range(len(a) - n):
a.pop()
def normal_convolution(a, b):
n = max(len(a) + len(b) - 1, 1)
c = [0] * n
for idx1, i in enumerate(a):
for idx2, j in enumerate(b):
c[idx1 + idx2] += i * j
return c
def normal_convolution_mod(a, b):
n = max(len(a) + len(b) - 1, 1)
c = [0] * n
for idx1, i in enumerate(a):
for idx2, j in enumerate(b):
c[idx1 + idx2] += i * j
for i in range(n):
c[i] %= mod
return c
class Fraction:
def __init__(self, num, den):
self.num = num
self.den = den
def __add__(self, other):
a_num = self.num
a_den = self.den
b_num = other.num
b_den = other.den
n2 = max(len(a_num) + len(b_num) - 1, 1)
if n2 < 16:
c_num = [(i + j ) % mod for i,j in zip(normal_convolution(a_num, b_den), normal_convolution(b_num, a_den))]
c_den = normal_convolution_mod(a_den, b_den)
else:
n = 1 << (n2-1).bit_length()
zero_pad(a_num, n)
zero_pad(a_den, n)
zero_pad(b_num, n)
zero_pad(b_den, n)
w_root = pow(3, (mod-1)//n, mod)
w = [1] * n
for i in range(1, n):
w[i] = w[i-1] * w_root % mod
fft_inplace(a_num, w)
fft_inplace(a_den, w)
fft_inplace(b_num, w)
fft_inplace(b_den, w)
c_num = [(a * d + b * c) % mod for a, b, c, d in zip(a_num, a_den, b_num, b_den)]
c_den = [a * b % mod for a, b in zip(a_den, b_den)]
ifft_inplace(c_num, w)
ifft_inplace(c_den, w)
zero_remove(c_num, n)
zero_remove(c_den, n)
return Fraction(c_num, c_den)
n, s = map(int, input().split())
s_inv = pow(s, mod-2, mod)
p = [i * s_inv % mod for i in map(int, input().split())]
fractions = collections.deque(
Fraction([0, i ** 2 % mod], [1, i]) for i in p
)
while len(fractions) > 1:
fractions.append(fractions.popleft() + fractions.popleft())
ans = 0
factorial = 2
for i in range(1, n + 1):
ans += fractions[0].num[i] * factorial % mod
factorial = factorial * (i + 2) % mod
ans %= mod
print(ans)
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