結果
| 問題 | No.2613 Sum of Combination |
| ユーザー |
 chineristAC
|
| 提出日時 | 2024-01-19 21:51:26 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 826 ms / 4,500 ms |
| コード長 | 8,188 bytes |
| コンパイル時間 | 317 ms |
| コンパイル使用メモリ | 82,444 KB |
| 実行使用メモリ | 159,884 KB |
| 最終ジャッジ日時 | 2024-09-28 04:21:37 |
| 合計ジャッジ時間 | 22,747 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / 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 | 62 ms
68,756 KB |
| testcase_01 | AC | 63 ms
68,984 KB |
| testcase_02 | AC | 139 ms
84,612 KB |
| testcase_03 | AC | 61 ms
68,644 KB |
| testcase_04 | AC | 66 ms
69,076 KB |
| testcase_05 | AC | 61 ms
68,536 KB |
| testcase_06 | AC | 62 ms
69,320 KB |
| testcase_07 | AC | 63 ms
70,296 KB |
| testcase_08 | AC | 116 ms
83,096 KB |
| testcase_09 | AC | 70 ms
73,700 KB |
| testcase_10 | AC | 62 ms
70,620 KB |
| testcase_11 | AC | 97 ms
82,612 KB |
| testcase_12 | AC | 97 ms
82,648 KB |
| testcase_13 | AC | 144 ms
84,492 KB |
| testcase_14 | AC | 145 ms
84,772 KB |
| testcase_15 | AC | 147 ms
84,024 KB |
| testcase_16 | AC | 146 ms
84,620 KB |
| testcase_17 | AC | 151 ms
84,704 KB |
| testcase_18 | AC | 141 ms
84,228 KB |
| testcase_19 | AC | 147 ms
84,892 KB |
| testcase_20 | AC | 112 ms
82,612 KB |
| testcase_21 | AC | 90 ms
79,952 KB |
| testcase_22 | AC | 173 ms
88,308 KB |
| testcase_23 | AC | 748 ms
151,104 KB |
| testcase_24 | AC | 738 ms
150,460 KB |
| testcase_25 | AC | 701 ms
144,612 KB |
| testcase_26 | AC | 810 ms
158,760 KB |
| testcase_27 | AC | 443 ms
122,972 KB |
| testcase_28 | AC | 789 ms
159,008 KB |
| testcase_29 | AC | 776 ms
154,840 KB |
| testcase_30 | AC | 784 ms
158,976 KB |
| testcase_31 | AC | 764 ms
153,212 KB |
| testcase_32 | AC | 749 ms
152,424 KB |
| testcase_33 | AC | 781 ms
158,180 KB |
| testcase_34 | AC | 758 ms
157,864 KB |
| testcase_35 | AC | 813 ms
159,884 KB |
| testcase_36 | AC | 795 ms
159,368 KB |
| testcase_37 | AC | 803 ms
159,356 KB |
| testcase_38 | AC | 786 ms
157,496 KB |
| testcase_39 | AC | 777 ms
158,380 KB |
| testcase_40 | AC | 781 ms
158,208 KB |
| testcase_41 | AC | 800 ms
159,084 KB |
| testcase_42 | AC | 811 ms
158,476 KB |
| testcase_43 | AC | 826 ms
159,744 KB |
| testcase_44 | AC | 762 ms
158,012 KB |
| testcase_45 | AC | 64 ms
69,752 KB |
| testcase_46 | AC | 63 ms
69,968 KB |
| testcase_47 | AC | 62 ms
69,764 KB |
| testcase_48 | AC | 66 ms
70,752 KB |
| testcase_49 | AC | 64 ms
70,576 KB |
| testcase_50 | AC | 794 ms
158,080 KB |
| testcase_51 | AC | 751 ms
158,152 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 = 2*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 find_primitive_root(P):
while True:
g = random.randint(1,P-1)
tmp = [0] * P
tmp[1] = True
a = 1
while tmp[(a*g) % P] == 0:
tmp[(a * g) % P] = 1
a = (a * g) % P
if sum(tmp) == P-1:
return g
N,P = mi()
fact = [1] * (P)
inv = [1] * P
inv[0] = 0
for i in range(2,P):
fact[i] = i * fact[i-1] % P
inv[i] = (-inv[P % i]) * (P//i) % P
ifact = [inv[fact[i]] for i in range(P)]
g = find_primitive_root(P)
log_g = [-1] * P
for i in range(P-1):
log_g[pow(g,i,P)] = i
f = [0] * (P-1)
f[0] = 1
while N:
n = N % P
tmp = [0] * (P-1)
for k in range(n+1):
val = fact[n] * (ifact[k] * ifact[n-k] % P) % P
tmp[log_g[val]] += 1
f = convolution(f,tmp)
for i in range(P-1,len(f)):
f[i % (P-1)] += f[i]
f[i % (P-1)] %= mod
f = f[:P-1]
N //= P
res = 0
for i in range(P-1):
res += pow(g,i,P) * f[i] % mod
res %= mod
print(res)