結果
| 問題 |
No.1875 Flip Cards
|
| コンテスト | |
| ユーザー |
 chineristAC
|
| 提出日時 | 2022-03-11 23:16:11 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 6,086 ms / 10,000 ms |
| コード長 | 10,033 bytes |
| コンパイル時間 | 179 ms |
| コンパイル使用メモリ | 81,920 KB |
| 実行使用メモリ | 274,272 KB |
| 最終ジャッジ日時 | 2024-09-16 03:41:22 |
| 合計ジャッジ時間 | 28,690 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 7 |
ソースコード
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 inverse(f,limit):
assert(f[0]!=0)
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 integral(f,limit):
res = [0]+[(f[i] * inv[i+1]) % mod for i in range(len(f)-1)]
return res[:limit]
def diff(f,limit):
res = [(f[i+1] * (i+1)) % mod for i in range(len(f)-1)]+[0]
return res[:limit]
def log(f,limit):
res = convolution(diff(f,limit),inverse(f,limit))[:limit]
return integral(res,limit)
def exp(_f,limit):
f = [v for v in _f]
l = len(f)
L = 1<<((l-1).bit_length())
n = L.bit_length()-1
f = f[:L]
f+=[0]*(L-len(f))
res = [1]
for i in range(1,n+1):
res += [0]*2**(i-1)
g = log(res,2**i)
h = [(f[j]-g[j])%mod for j in range(2**i)]
h[0] = (h[0]+1) % mod
res =convolution(res,h)[:2**i]
return res[:limit]
import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import gcd
input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())
def plus(f,g):
res = [0] * (max(len(f),len(g)))
for i in range(len(f)):
res[i] += f[i]
res[i] %= mod
for i in range(len(g)):
res[i] += g[i]
res[i] %= mod
return res
def taylor_shift(f,N):
if len(f) <= N:
f += [0] * (N+1-len(f))
g = [0] * (N+1)
for i in range(N+1):
if i&1:
g[N-i] = (f[i]) * g1[i] % mod
else:
g[N-i] = (f[i]) * g1[i] % mod
ex = [0] * (N+1)
for i in range(N+1):
if i&1:
ex[i] = -g2[i] % mod
else:
ex[i] = g2[i] % mod
p = convolution(g,ex)
res = [0] * (N+1)
for i in range(N):
res[i] = p[N-i] * g2[i] % mod
return res
N,M = mi()
card = [tuple(mi()) for i in range(N)]
prod = 1
for a,b,c in card:
prod *= pow(a,c,mod) % mod
prod %= mod
deq = deque([])
for a,b,c in card:
d = b * pow(a,mod-2,mod) % mod
deq.append([[c*d%mod],[1,(d)%mod]])
while len(deq) > 1:
fp,fq = deq.popleft()
gp,gq = deq.popleft()
hp,hq = plus(convolution(fp,gq),convolution(gp,fq)),convolution(fq,gq)
deq.append([hp,hq])
p,q = deq.popleft()
q += [0] * M
q = inverse(q,M+1)
last = convolution(p,q)[:M+1]
log_f = integral(last,M+1)
f = exp(log_f,M+1)
f = [prod * v % mod for v in f]
f = taylor_shift(f,M+1)
deq = deque([])
for i in range(M+1):
deq.append(([[f[i]],[1,(-i)%mod]]))
while len(deq) > 1:
fp,fq = deq.popleft()
gp,gq = deq.popleft()
hp,hq = plus(convolution(fp,gq),convolution(gp,fq)),convolution(fq,gq)
deq.append([hp,hq])
p,q = deq.popleft()
q += [0] * M
q = inverse(q,M+1)
last = convolution(p,q)[:M+1]
for i in range(1,M+1):
print(last[i])