結果

問題 No.2108 Red or Blue and Purple Tree
ユーザー chineristACchineristAC
提出日時 2022-10-21 23:06:07
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,690 ms / 4,000 ms
コード長 8,288 bytes
コンパイル時間 401 ms
コンパイル使用メモリ 87,152 KB
実行使用メモリ 184,264 KB
最終ジャッジ日時 2023-09-13 23:14:50
合計ジャッジ時間 26,144 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge12
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 2,458 ms
182,056 KB
testcase_01 AC 2,690 ms
183,232 KB
testcase_02 AC 2,684 ms
183,680 KB
testcase_03 AC 2,602 ms
183,580 KB
testcase_04 AC 2,611 ms
184,264 KB
testcase_05 AC 2,639 ms
183,476 KB
testcase_06 AC 2,646 ms
183,180 KB
testcase_07 AC 2,616 ms
183,672 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 # 

import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import combinations, permutations
from math import log,gcd




input = lambda :sys.stdin.buffer.readline()
mi = lambda :map(int,input().split())
li = lambda :list(mi())


def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    return (g1[n] * g2[r] % mod) * g2[n-r] % mod

mod = 998244353
N = 2*10**5
g1 = [1]*(N+1)
g2 = [1]*(N+1)
inverse = [1]*(N+1)

for i in range( 2, N + 1 ):
    g1[i]=( ( g1[i-1] * i ) % mod )
    inverse[i]=( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2[i]=( (g2[i-1] * inverse[i]) % mod )
inverse[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))]

N = 2000
dp = [[0]*(N+1) for i in range(N+1)]
dp[0][0] = 1
tmp = [0] + [pow(i,i,mod)*g2[i]%mod for i in range(1,N+1)]
for k in range(1,N+1):
    dp[k] = convolution(dp[k-1],tmp)[:N+1]

exp = [g2[i]*pow(-1,i,mod) % mod for i in range(N+1)]

def calc(N):
    f = [dp[N-k][N]*(g1[N]*g2[N-k] % mod) % mod for k in range(N)]
    t = pow(N,2*N-2,mod)
    for k in range(N):
        t = (t * (inverse[N] * inverse[N] % mod)) % mod
        f[k] = f[k] * t % mod
        
    f = [f[i]*g1[i] % mod for i in range(N)][::-1]
    
    g = convolution(f,exp[:N])[:N]
    
    g = g[::-1]
    g = [g[i]*g2[i]%mod for i in range(N)]
    
    return g

ans = [[]] + [calc(i) for i in range(1,N+1)]

for _ in range(int(input())):
    n,k = mi()
    print(ans[n][k])
0