結果

問題 No.1875 Flip Cards
ユーザー chineristACchineristAC
提出日時 2022-03-11 23:16:11
言語 PyPy3
(7.3.13)
結果
AC  
実行時間 5,452 ms / 10,000 ms
コード長 10,033 bytes
コンパイル時間 760 ms
コンパイル使用メモリ 87,088 KB
実行使用メモリ 277,104 KB
最終ジャッジ日時 2023-10-14 08:33:23
合計ジャッジ時間 27,009 ms
ジャッジサーバーID
(参考情報)
judge14 / judge13
このコードへのチャレンジ(β)

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 123 ms
82,520 KB
testcase_01 AC 112 ms
82,676 KB
testcase_02 AC 121 ms
83,108 KB
testcase_03 AC 1,514 ms
163,976 KB
testcase_04 AC 2,868 ms
259,524 KB
testcase_05 AC 3,960 ms
261,048 KB
testcase_06 AC 5,332 ms
276,300 KB
testcase_07 AC 5,452 ms
276,868 KB
testcase_08 AC 5,363 ms
277,104 KB
testcase_09 AC 130 ms
83,364 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

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])



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