結果
| 問題 |
No.3273 Exactly One Match
|
| コンテスト | |
| ユーザー |
 apricity
|
| 提出日時 | 2025-08-10 22:23:15 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 3,072 ms / 4,000 ms |
| コード長 | 5,945 bytes |
| コンパイル時間 | 591 ms |
| コンパイル使用メモリ | 82,292 KB |
| 実行使用メモリ | 371,948 KB |
| 最終ジャッジ日時 | 2025-09-12 23:48:40 |
| 合計ジャッジ時間 | 6,910 ms |
|
ジャッジサーバーID （参考情報） |
judge7 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 26 |
ソースコード
# https://judge.yosupo.jp/submission/55648
# AtCoder Libary v1.4 を python に移植したもの
# https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp
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 butterfly(a):
n = len(a)
h = (n - 1).bit_length()
le = 0
while le < h:
if h - le == 1:
p = 1 << (h - le - 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 butterfly_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 multiply(s, t):
n = len(s)
m = len(t)
if min(n, m) <= 60:
a = [0] * (n + m - 1)
for i in range(n):
if i % 8 == 0:
for j in range(m):
a[i + j] += s[i] * t[j]
a[i + j] %= MOD
else:
for j in range(m):
a[i + j] += s[i] * t[j]
return [x % MOD for x in a]
a = s.copy()
b = t.copy()
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
b += [0] * (z - m)
butterfly(a)
butterfly(b)
for i in range(z):
a[i] *= b[i]
a[i] %= MOD
butterfly_inv(a)
a = a[:n + m - 1]
iz = pow(z, MOD - 2, MOD)
return [v * iz % MOD for v in a]
N, K = map(int, input().split())
if K == 1:
print(1 if N == 1 else 0)
exit(0)
fact = [0 for _ in range(N+2)]
finv = [0 for _ in range(N+2)]
inv = [0 for _ in range(N+2)]
fact[0] = fact[1] = 1
finv[0] = finv[1] = 1
inv[1] = 1
for i in range(2, N+2):
fact[i] = fact[i-1] * i % MOD
inv[i] = MOD - inv[MOD%i] * (MOD//i)
finv[i] = finv[i-1] * inv[i] % MOD
kp = [0 for _ in range(N+1)]
np = [0 for _ in range(N+1)]
f = [0 for _ in range(N+1)]
tk = tn = 1
ni = pow(N, MOD-2, MOD)
coef = 1
for i in range(N+1):
kp[i] = tk
tk = tk * (K-1) % MOD
np[i] = tn
tn = tn * ni % MOD
f[i] = coef * (-1 if i%2 else 1) % MOD
coef = coef * inv[i+1] * (K-1+i) % MOD
g = multiply(kp,f)[:N+1]
ans = 0
for s in range(N):
ans += g[s] * s * kp[N-s-1] * finv[N-s-1] * np[s]
ans %= MOD
a = [kp[i] + (K-1) * (-1 if i%2 else 1) % MOD for i in range(N+1)]
h = multiply(a,g)
for s in range(1,N+1):
ans += h[s-1] * s * kp[N-s] * finv[N-s] * np[s]
ans %= MOD
ans *= fact[N] * pow(N, N-1, MOD)
ans %= MOD
print(ans)