結果
| 問題 | No.3480 Prefix Advantage |
| コンテスト | |
| ユーザー |
👑  potato167
|
| 提出日時 | 2026-03-20 03:43:52 |
| 言語 | PyPy3 (7.3.17) |
| 結果 |
AC
|
| 実行時間 | 626 ms / 2,000 ms |
| コード長 | 6,610 bytes |
| 記録 | |
| コンパイル時間 | 727 ms |
| コンパイル使用メモリ | 85,696 KB |
| 実行使用メモリ | 221,532 KB |
| 最終ジャッジ日時 | 2026-03-20 20:58:29 |
| 合計ジャッジ時間 | 41,457 ms |
|
ジャッジサーバーID （参考情報） |
judge1_1 / judge2_0 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 60 |
ソースコード
import sys
# https://judge.yosupo.jp/submission/222202
mod = 998244353
imag = 911660635
iimag = 86583718
rate2 = (0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0)
irate2 = (0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0)
rate3 = (0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0)
irate3 = (0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0)
def fft(a):
n = len(a)
h = (n - 1).bit_length()
le = 0
while le < h:
if h == le + 1:
p = 1
rot = 1
for s in range(1 << le):
offset = s << (h - le)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p] * rot
a[i + offset] = (l + r) % mod
a[i + offset + p] = (l - r) % mod
rot *= rate2[(~s & -~s).bit_length()]
rot %= mod
le += 1
else:
p = 1 << (h - le - 2)
rot = 1
for s in range(1 << le):
rot2 = rot * rot % mod
rot3 = rot2 * rot % mod
offset = s << (h - le)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p] * rot
a2 = a[i + offset + p * 2] * rot2
a3 = a[i + offset + p * 3] * rot3
a1na3imag = (a1 - a3) % mod * imag
a[i + offset] = (a0 + a2 + a1 + a3) % mod
a[i + offset + p] = (a0 + a2 - a1 - a3) % mod
a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % mod
a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % mod
rot *= rate3[(~s & -~s).bit_length()]
rot %= mod
le += 2
def fft_inv(a):
n = len(a)
h = (n - 1).bit_length()
le = h
while le:
if le == 1:
p = 1 << (h - le)
irot = 1
for s in range(1 << (le - 1)):
offset = s << (h - le + 1)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p]
a[i + offset] = (l + r) % mod
a[i + offset + p] = (l - r) * irot % mod
irot *= irate2[(~s & -~s).bit_length()]
irot %= mod
le -= 1
else:
p = 1 << (h - le)
irot = 1
for s in range(1 << (le - 2)):
irot2 = irot * irot % mod
irot3 = irot2 * irot % mod
offset = s << (h - le + 2)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p]
a2 = a[i + offset + p * 2]
a3 = a[i + offset + p * 3]
a2na3iimag = (a2 - a3) * iimag % mod
a[i + offset] = (a0 + a1 + a2 + a3) % mod
a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % mod
a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % mod
a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % mod
irot *= irate3[(~s & -~s).bit_length()]
irot %= mod
le -= 2
def ntt(a):
if len(a) <= 1:
return
fft(a)
def ntt_inv(a):
if len(a) <= 1:
return
fft_inv(a)
iv = pow(len(a),mod-2,mod)
for i in range(len(a)):
a[i] = a[i] * iv % mod
def convolute(a,b):
aa = a[:]
bb = b[:]
n = len(aa)
m = len(bb)
z = 1 << (n + m - 2).bit_length()
aa += [0] * (z - n)
bb += [0] * (z - m)
fft(aa)
fft(bb)
for i in range(z):
aa[i] = aa[i] * bb[i] % mod
fft_inv(aa)
aa = aa[:n + m - 1]
iz = pow(z, mod - 2, mod)
for i in range(n+m-1):
aa[i] = (aa[i] * iz) % mod
return aa
MOD = 998244353
class Binomial:
def __init__(self, max_n: int = 0):
self.fact = [1]
self.fact_inv = [1]
self.extend(max_n + 1)
def extend(self, m: int = -1) -> None:
n = len(self.fact)
if m == -1:
m = n * 2
if n >= m:
return
self.fact += [1] * (m - n)
self.fact_inv += [1] * (m - n)
for i in range(n, m):
self.fact[i] = self.fact[i - 1] * i % MOD
self.fact_inv[m - 1] = pow(self.fact[m - 1], MOD - 2, MOD)
for i in range(m - 1, n, -1):
self.fact_inv[i - 1] = self.fact_inv[i] * i % MOD
def fact_val(self, i: int) -> int:
if i < 0:
return 0
while len(self.fact) <= i:
self.extend()
return self.fact[i]
def invfact(self, i: int) -> int:
if i < 0:
return 0
while len(self.fact_inv) <= i:
self.extend()
return self.fact_inv[i]
def C(self, a: int, b: int) -> int:
if a < b or b < 0:
return 0
return self.fact_val(a) * self.invfact(b) % MOD * self.invfact(a - b) % MOD
def inv(self, a: int) -> int:
if a < 0:
return (-self.inv(-a)) % MOD
if a == 0:
return 1
return self.fact_val(a - 1) * self.invfact(a) % MOD
def solve_fast_2(N: int, P: int, Q: int):
table = Binomial()
tmp = [0] * (N + 1)
for i in range(1, N + 1):
tmp[i] = (
table.C(P - 1, i - 1)
* table.C(Q - 1, i - 1)
% MOD
* table.inv(i)
% MOD
)
nx = [0] * (N + 1)
for i in range(N + 1):
nx[i] = table.C(P + Q + i, i)
tmp = convolute(tmp, nx)
tmp = tmp[:N + 1]
return tmp
def main() -> None:
input = sys.stdin.readline
N, P, Q = map(int, input().split())
ans = solve_fast_2(N, P, Q)
print(*ans[1:], sep="\n")
if __name__ == "__main__":
main()