結果

問題 No.2959 Dolls' Tea Party
ユーザー 👑 binap
提出日時 2024-10-28 17:17:47
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,400 ms / 3,000 ms
コード長 9,198 bytes
コンパイル時間 331 ms
コンパイル使用メモリ 82,608 KB
実行使用メモリ 175,116 KB
最終ジャッジ日時 2024-10-29 00:10:35
合計ジャッジ時間 67,384 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 4
other AC * 33
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 #
プレゼンテーションモードにする

import math
from collections import defaultdict
# pow/log/exp of FPS
# thanks for https://judge.yosupo.jp/submission/126665
# FFT
# code from: https://atcoder.jp/contests/practice2/submissions/24974537
# but changed a little
_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):
    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)
# ----
# 1/F
# 必要 : a[0] != 0
# 前提 : FFT
def poly_inv(a, length = None):
    if length == None: M = len(a)
    else: M = length
    if M <= 0: return []
    n = len(a)
    r = pow(a[0], _fft_mod-2, _fft_mod)
    m = 1
    res = [r]
    while m < M:
        f = a[:min(n,2*m)] + [0]*(2*m-min(n,2*m))
        g = res + [0]*m
        _butterfly(f)
        _butterfly(g)
        for i in range(2*m):
            f[i] = f[i] * g[i] % _fft_mod
        _butterfly_inv(f)
        f = f[m:] + [0]*m
        _butterfly(f)
        for i in range(2*m):
            f[i] = f[i] * g[i] % _fft_mod
        _butterfly_inv(f)
        iz = pow(2*m, _fft_mod-2, _fft_mod)
        iz = (-iz*iz) % _fft_mod
        for i in range(m):
            f[i] = f[i] * iz % _fft_mod
        res += f[:m]
        m <<= 1
    return res[:M]
# 多点評価
# x に評価したい点を配列で入れよう！
def multi_eval(x, a):
    n = len(x)
    siz = 1 << (n-1).bit_length()
    g = [[1] for i in range(2 * siz)]
    for i in range(n):
        g[i + siz] = [-x[i], 1]
    for i in range(siz-1, 0, -1):
        g[i] = convolution(g[2 * i], g[2 * i + 1])
    
    for i in range(1, 2 * siz):
        if i == 1: f = a[::]
        else: f = g[i >> 1]
        m = len(f) - len(g[i]) + 1
        v = convolution(f[::-1][:m], poly_inv(g[i][::-1], m))[m-1::-1]
        w = convolution(v, g[i])
        g[i] = f[::]
        h = g[i]
        for j in range(len(w)):
            h[j] -= w[j]
            h[j] %= _fft_mod
        
        while len(h) > 1 and h[-1] == 0:
            h.pop()
    
    return [g[i+siz][0] for i in range(n)]
# DEF MOD FACT
mod = _fft_mod
N = 10**6 + 5
fact = [1]*(N+1)
factinv = [1]*(N+1)
for i in range(2, N+1):
    fact[i] = fact[i-1] * i % mod
factinv[-1] = pow(fact[-1], mod-2, mod)
for i in range(N-1, 1, -1):
    factinv[i] = factinv[i+1] * (i+1) % mod
def cmb(a, b):
    if (a < b) or (b < 0): return 0
    return fact[a] * factinv[b] % mod * factinv[a-b] % mod
# log(F)
# 必要 : a[0] = 1
# 前提 : FFT, inv
def poly_log(a, length = None):
    if length == None: M = len(a)
    else: M = length
    if M <= 0: return []
    n = len(a)
    if n == 1: return [0] * M
    b = [a[i+1] * (i+1) % _fft_mod for i in range(n-1)]
    t = convolution(b, poly_inv(a, length = M))
    return [0] + [t[i] * factinv[i+1] % _fft_mod * fact[i] % _fft_mod for i in range(M-1)]
# exp(F)
# 必要 : a[0] = 0
# 前提 : FFT, inv, log
def poly_exp(a, length = None):
    if length == None: M = len(a)
    else: M = length
    if M <= 0: return []
    n = len(a)
    m = 1
    res = [1]
    while m < M:
        f = a[:min(n,2*m)] + [0]*(2*m-min(n,2*m))
        #print(res)
        v = poly_log(res, length = 2*m)
        w = [(f[i]-v[i])%_fft_mod for i in range(2*m)]
        w[0] = (w[0]+1)%_fft_mod
        g = convolution(res, w)
        res += g[m:2*m]
        m <<= 1
    return res[:M]
def poly_pow_nonzero(a, m, l):
    n = len(a)
    bais = pow(a[0], m, _fft_mod)
    invs = pow(a[0], _fft_mod-2, _fft_mod)
    r = [a[i] * invs % _fft_mod for i in range(n)]
    r = poly_log(r, length = l)
    for i in range(l):
        r[i] = r[i] * m % _fft_mod
    r = poly_exp(r, length = l)
    for i in range(l):
        r[i] = r[i] * bais % _fft_mod
    return r
def poly_pow(a, m, l):
    n = len(a)
    ind = 0
    for i in range(n):
        if a[i] != 0:
            ind = i
            break
    if ind * m >= l:
        return [0] * l
    return [0] * (ind * m) + poly_pow_nonzero(a[ind:], m, l-ind*m)
# DEF MOD FACT はされています！！6
MOD = 998244353
def main():
    N, K = map(int,input().split())
    A = list(map(int,input().split()))
    
    Frequency_P = defaultdict(int)
    for i in range(K):
        Frequency_P[math.gcd(i + 1, K)] += 1
    
    Frequency_A = [0] * (K + 1)
    for i in range(N):
        Frequency_A[min(A[i], K)] += 1
    facts = [1] * (K + 1)
    ifacts = [1] * (K + 1)
    for i in range(K):
        facts[i + 1] = facts[i] * (i + 1) % MOD
        ifacts[i + 1] = pow(facts[i + 1], MOD - 2, MOD)
    
    F = [[0 for i in range(K + 1)] for j in range(K + 1)]
    F_log = [[0 for i in range(K + 1)] for j in range(K + 1)]
    for i in range(K + 1):
        for j in range(i + 1):
            F[i][j] = ifacts[j]
        F_log[i] = poly_log(F[i])
    
    ans = 0
    for P, C in Frequency_P.items():
        Q = K // P
        Frequency_B = [0] * (P + 1)
        for i in range(K + 1):
            Frequency_B[i // Q] += Frequency_A[i]
        G_log = [0] * (P + 1)
        for i in range(P + 1):
            for j in range(P + 1):
                G_log[j] += F_log[i][j] * Frequency_B[i]
        for j in range(P + 1):
            G_log[j] %= MOD
        G = poly_exp(G_log)
        ans += G[P] * facts[P] * C
        
    ans *= pow(K, MOD - 2, MOD)
    ans %= MOD
    print(ans)
    
    
main()
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0