結果
| 問題 |
No.3376 Rectangle in Circle
|
| コンテスト | |
| ユーザー |
 lif4635
|
| 提出日時 | 2025-10-18 21:19:50 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
MLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 7,172 bytes |
| コンパイル時間 | 159 ms |
| コンパイル使用メモリ | 82,336 KB |
| 実行使用メモリ | 849,288 KB |
| 最終ジャッジ日時 | 2025-11-21 20:51:40 |
| 合計ジャッジ時間 | 2,155 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 1 MLE * 1 -- * 18 |
ソースコード
from array import array
MOD = 998244353
IMAG = 911660635
IIMAG = 86583718
INV2 = 499122177
rate2 = array('I', [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 = array('I', [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 = array('I', [0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0])
irate3 = array('I', [0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0])
# https://judge.yosupo.jp/submission/55648
def butterfly(a: list):
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: list):
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: list, t: list):
n = len(s)
m = len(t)
if min(n, m) <= 60:
a = [0] * (n + m - 1)
for i in range(n):
if i&7 == 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]
def shrink(a: list):
while a and not a[-1]: a.pop()
mod = 998244353
class Comb:
__slots__ = ["fac", "finv", "mod"]
def __init__(self, lim:int, mod:int = mod):
"""
mod : prime
"""
self.fac = [1]*(lim+1)
self.finv = [1]*(lim+1)
self.mod = mod
for i in range(2,lim+1):
self.fac[i] = self.fac[i-1]*i%self.mod
self.finv[lim] = pow(self.fac[lim],-1,mod)
for i in range(lim,2,-1):
self.finv[i-1] = self.finv[i]*i%self.mod
def C(self, a, b):
if b < 0 or a < b: return 0
if a < 0: return 0
return self.fac[a]*self.finv[b]%self.mod*self.finv[a-b]%self.mod
def __call__(self, a, b):
if b < 0 or a < b: return 0
if a < 0: return 0
return self.fac[a]*self.finv[b]%self.mod*self.finv[a-b]%self.mod
def P(self, a, b):
if b < 0 or a < b: return 0
if a < 0: return 0
return self.fac[a]*self.finv[a-b]%self.mod
def H(self, a, b): return self.C(a+b-1,b)
def F(self, a): return self.fac[a]
def Fi(self, a): return self.finv[a]
lim = 10000
comb = Comb(lim)
p2 = [1] * (lim + 1)
for i in range(lim):
p2[i+1] = 2 * p2[i] % mod
def solve():
n, l = map(int, input().split())
d = list(map(int, input().split()))
if l & 1:
ans = 0
for i in range(n):
ans += pow(n - i, -1, mod)
ans %= mod
print(n * ans % mod)
return
h = l // 2
c = [0] * h
for x in d:
c[x%h] += 1
c1 = c.count(1)
c2 = c.count(2)
f = [0] * (c1 + 1)
for p in range(c1 + 1):
f[p] = comb.Fi(p) * comb.Fi(c1 - p) % mod
g = [0] * (c2 + 2)
for q in range(c2 + 2):
if 0 <= q <= c2:
g[q] += comb.Fi(c2 - q) * p2[q] % mod
if 2 <= q <= c2+1:
g[q] += q * (q - 1) * comb.Fi(c2-1 - (q-2)) * p2[q-2] % mod
g[q] = g[q] * comb.Fi(q) % mod
r = multiply(f, g)
ans = 0
for i in range(min(len(r), n)):
ans += r[i] * comb.F(n - i) % mod * comb.F(i) % mod * pow(n - i, -1, mod) % mod
print(ans * comb.F(c1) % mod * comb.F(c2) % mod * comb.Fi(n) % mod * n % mod)
return
t = int(input())
for i in range(t):
solve()