結果
| 問題 | No.2661 Sweep Cards (Hard) |
| ユーザー |
 chineristAC
|
| 提出日時 | 2024-02-24 12:05:53 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 1,359 ms / 4,000 ms |
| コード長 | 8,805 bytes |
| コンパイル時間 | 433 ms |
| コンパイル使用メモリ | 82,048 KB |
| 実行使用メモリ | 254,184 KB |
| 最終ジャッジ日時 | 2024-09-29 11:11:13 |
| 合計ジャッジ時間 | 30,689 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 72 ms
76,976 KB |
| testcase_01 | AC | 71 ms
76,680 KB |
| testcase_02 | AC | 69 ms
76,344 KB |
| testcase_03 | AC | 73 ms
76,420 KB |
| testcase_04 | AC | 73 ms
76,708 KB |
| testcase_05 | AC | 75 ms
77,428 KB |
| testcase_06 | AC | 73 ms
77,044 KB |
| testcase_07 | AC | 70 ms
75,980 KB |
| testcase_08 | AC | 71 ms
76,520 KB |
| testcase_09 | AC | 72 ms
77,168 KB |
| testcase_10 | AC | 78 ms
78,616 KB |
| testcase_11 | AC | 93 ms
87,416 KB |
| testcase_12 | AC | 110 ms
89,700 KB |
| testcase_13 | AC | 108 ms
89,728 KB |
| testcase_14 | AC | 115 ms
89,672 KB |
| testcase_15 | AC | 143 ms
90,516 KB |
| testcase_16 | AC | 172 ms
93,308 KB |
| testcase_17 | AC | 662 ms
154,028 KB |
| testcase_18 | AC | 1,359 ms
252,780 KB |
| testcase_19 | AC | 1,102 ms
237,888 KB |
| testcase_20 | AC | 1,117 ms
238,416 KB |
| testcase_21 | AC | 1,171 ms
237,688 KB |
| testcase_22 | AC | 1,146 ms
234,792 KB |
| testcase_23 | AC | 1,149 ms
235,180 KB |
| testcase_24 | AC | 1,110 ms
234,352 KB |
| testcase_25 | AC | 1,125 ms
234,316 KB |
| testcase_26 | AC | 1,134 ms
237,836 KB |
| testcase_27 | AC | 1,118 ms
237,964 KB |
| testcase_28 | AC | 1,136 ms
234,772 KB |
| testcase_29 | AC | 1,126 ms
238,348 KB |
| testcase_30 | AC | 1,203 ms
253,536 KB |
| testcase_31 | AC | 1,195 ms
254,184 KB |
| testcase_32 | AC | 1,204 ms
253,820 KB |
| testcase_33 | AC | 1,133 ms
238,820 KB |
| testcase_34 | AC | 1,188 ms
246,264 KB |
| testcase_35 | AC | 1,281 ms
253,948 KB |
| testcase_36 | AC | 1,281 ms
254,100 KB |
| testcase_37 | AC | 1,180 ms
246,204 KB |
| testcase_38 | AC | 1,296 ms
253,652 KB |
| testcase_39 | AC | 1,275 ms
253,924 KB |
ソースコード
import sys
from itertools import permutations
from heapq import heappop,heappush
from collections import deque
import random
import bisect
from math import gcd
input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())
mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)
N = 5*10**5
g1 = [1]*(N+1) # 元テーブル
g2 = [1]*(N+1) #逆元テーブル
inv = [1]*(N+1) #逆元テーブル計算用テーブル
for i in range( 2, N + 1 ):
g1[i]=( ( g1[i-1] * i ) % mod )
inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod )
g2[i]=( (g2[i-1] * inv[i]) % mod )
inv[0]=0
_fft_mod = 998244353
_fft_imag = 911660635
_fft_iimag = 86583718
_fft_rate2 = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899)
_fft_irate2 = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960,
354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235)
_fft_rate3 = (372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,
183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204)
_fft_irate3 = (509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500,
771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681)
def _butterfly(a):
n = len(a)
h = (n - 1).bit_length()
len_ = 0
while len_ < h:
if h - len_ == 1:
p = 1 << (h - len_ - 1)
rot = 1
for s in range(1 << len_):
offset = s << (h - len_)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p] * rot % _fft_mod
a[i + offset] = (l + r) % _fft_mod
a[i + offset + p] = (l - r) % _fft_mod
if s + 1 != (1 << len_):
rot *= _fft_rate2[(~s & -~s).bit_length() - 1]
rot %= _fft_mod
len_ += 1
else:
p = 1 << (h - len_ - 2)
rot = 1
for s in range(1 << len_):
rot2 = rot * rot % _fft_mod
rot3 = rot2 * rot % _fft_mod
offset = s << (h - len_)
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) % _fft_mod * _fft_imag
a[i + offset] = (a0 + a2 + a1 + a3) % _fft_mod
a[i + offset + p] = (a0 + a2 - a1 - a3) % _fft_mod
a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % _fft_mod
a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % _fft_mod
if s + 1 != (1 << len_):
rot *= _fft_rate3[(~s & -~s).bit_length() - 1]
rot %= _fft_mod
len_ += 2
def _butterfly_inv(a):
n = len(a)
h = (n - 1).bit_length()
len_ = h
while len_:
if len_ == 1:
p = 1 << (h - len_)
irot = 1
for s in range(1 << (len_ - 1)):
offset = s << (h - len_ + 1)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p]
a[i + offset] = (l + r) % _fft_mod
a[i + offset + p] = (l - r) * irot % _fft_mod
if s + 1 != (1 << (len_ - 1)):
irot *= _fft_irate2[(~s & -~s).bit_length() - 1]
irot %= _fft_mod
len_ -= 1
else:
p = 1 << (h - len_)
irot = 1
for s in range(1 << (len_ - 2)):
irot2 = irot * irot % _fft_mod
irot3 = irot2 * irot % _fft_mod
offset = s << (h - len_ + 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) * _fft_iimag % _fft_mod
a[i + offset] = (a0 + a1 + a2 + a3) % _fft_mod
a[i + offset + p] = (a0 - a1 +
a2na3iimag) * irot % _fft_mod
a[i + offset + p * 2] = (a0 + a1 -
a2 - a3) * irot2 % _fft_mod
a[i + offset + p * 3] = (a0 - a1 -
a2na3iimag) * irot3 % _fft_mod
if s + 1 != (1 << (len_ - 1)):
irot *= _fft_irate3[(~s & -~s).bit_length() - 1]
irot %= _fft_mod
len_ -= 2
def _convolution_naive(a, b):
n = len(a)
m = len(b)
ans = [0] * (n + m - 1)
if n < m:
for j in range(m):
for i in range(n):
ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
else:
for i in range(n):
for j in range(m):
ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
return ans
def _convolution_fft(a, b):
a = a.copy()
b = b.copy()
n = len(a)
m = len(b)
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
_butterfly(a)
b += [0] * (z - m)
_butterfly(b)
for i in range(z):
a[i] = a[i] * b[i] % _fft_mod
_butterfly_inv(a)
a = a[:n + m - 1]
iz = pow(z, _fft_mod - 2, _fft_mod)
for i in range(n + m - 1):
a[i] = a[i] * iz % _fft_mod
return a
def _convolution_square(a):
a = a.copy()
n = len(a)
z = 1 << (2 * n - 2).bit_length()
a += [0] * (z - n)
_butterfly(a)
for i in range(z):
a[i] = a[i] * a[i] % _fft_mod
_butterfly_inv(a)
a = a[:2 * n - 1]
iz = pow(z, _fft_mod - 2, _fft_mod)
for i in range(2 * n - 1):
a[i] = a[i] * iz % _fft_mod
return a
def convolution(a, b):
"""It calculates (+, x) convolution in mod 998244353.
Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1],
it calculates the array c of length n + m - 1, defined by
> c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353.
It returns an empty list if at least one of a and b are empty.
Constraints
-----------
> len(a) + len(b) <= 8388609
Complexity
----------
> O(n log n), where n = len(a) + len(b).
"""
n = len(a)
m = len(b)
if n == 0 or m == 0:
return []
if min(n, m) <= 0:
return _convolution_naive(a, b)
if a is b:
return _convolution_square(a)
return _convolution_fft(a, b)
def taylor_shift(f,a):
g = [f[i]*g1[i]%mod for i in range(len(f))][::-1]
e = [g2[i] for i in range(len(f))]
t = 1
for i in range(1,len(f)):
t = t * a % mod
e[i] = e[i] * t % mod
res = convolution(g,e)[:len(f)]
return [res[len(f)-1-i]*g2[i]%mod for i in range(len(f))]
def fps_pow(f,K,N):
res = [1]
g = f[:]
while K:
if K & 1:
res = convolution(g,res)[:N]
g = convolution(g,g)[:N]
K >>= 1
return res
def inverse(f,limit):
assert(f[0]!=0)
f += [0] * (limit-len(f))
l = len(f)
L = 1<<((l-1).bit_length())
n = L.bit_length()-1
f = f[:L]
f+=[0]*(L-len(f))
res = [pow(f[0],mod-2,mod)]
for i in range(1,n+1):
h = convolution(res,f[:2**i])[:2**i]
h = [(-h[i]) % mod for i in range(2**i)]
h[0] = (h[0]+2) % mod
res = convolution(res,h)[:2**i]
return res[:limit]
def cmb(n,r,mod):
if r < 0 or n < r:
return 0
return g1[n] * (g2[r] * g2[n-r] % mod) % mod
def calc3(N,K):
h = [0] * (N+2)
for n in range(1,N+2):
if (n-1) % (K-1):
continue
Q = (n-1) // (K-1)
if Q & 1:
h[n] = -cmb(n,Q,mod) * inv[n] % mod
else:
h[n] = cmb(n,Q,mod) * inv[n] % mod
f = [2*h[n] % mod for n in range(1,N+2)]
f[0] = 1
inv_f = inverse(f,N+1)
g = fps_pow(inv_f,N,N+1)
res = [g[N-k] * (k * inv[N] % mod) % mod for k in range(N+1)]
return res[:]
N,K,M = mi()
X = li()
res = calc3(N,K)
for k in range(M):
print(res[X[k]])