#1025657 (PyPy3) No.2959 Dolls' Tea Party

提出ソース

結果

問題	No.2959 Dolls' Tea Party
ユーザー	vwxyz
提出日時	2024-11-09 00:27:01
言語	PyPy3 (7.3.15)
結果	WA
実行時間	-
コード長	9,014 bytes
コンパイル時間	726 ms
コンパイル使用メモリ	81,920 KB
実行使用メモリ	269,628 KB
最終ジャッジ日時	2024-11-09 00:28:27
合計ジャッジ時間	48,723 ms
ジャッジサーバーID （参考情報）	judge4 / judge2

このコードへのチャレンジ
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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	WA	-
testcase_01	WA	-
testcase_02	WA	-
testcase_03	WA	-
testcase_04	WA	-
testcase_05	WA	-
testcase_06	WA	-
testcase_07	WA	-
testcase_08	WA	-
testcase_09	TLE	-
testcase_10	TLE	-
testcase_11	TLE	-
testcase_12	TLE	-
testcase_13	TLE	-
testcase_14	WA	-
testcase_15	WA	-
testcase_16	TLE	-
testcase_17	TLE	-
testcase_18	TLE	-
testcase_19	TLE	-
testcase_20	TLE	-
testcase_21	WA	-
testcase_22	WA	-
testcase_23	WA	-
testcase_24	AC	89 ms 80,000 KB
testcase_25	AC	89 ms 79,744 KB
testcase_26	WA	-
testcase_27	AC	2,356 ms 129,648 KB
testcase_28	AC	2,506 ms 130,148 KB
testcase_29	WA	-
testcase_30	WA	-
testcase_31	WA	-
testcase_32	WA	-
testcase_33	WA	-
testcase_34	WA	-
testcase_35	TLE	-
testcase_36	TLE	-

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ソースコード

raw source code

import math
from functools import lru_cache
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)

N,K=map(int,input().split())
A=tuple(map(int,input().split()))
mod=998244353
fact=[1]
for i in range(1,N+K+1):
    fact.append(fact[-1]*i%mod)
fact_inve=[pow(fact[i],mod-2,mod) for i in range(N+K+1)]
ans=0
memo_log=[poly_log([fact_inve[x] if x<=c else 0 for x in range(K+1)]) for c in range(K+1)]
@lru_cache(maxsize=None)
def solve(C):
    S=K//C
    AA=[a for a in A]
    cnt=[0]*(C+2)
    for i in range(N):
        AA[i]//=S
        AA[i]=min(AA[i],C)
        if AA[i]:
            cnt[AA[i]]+=1
    poly_log=[0]*(C+1)
    for c in range(1,C+1):
        if cnt[c]:
            poly=memo_log[min(c,C)]
            for x in range(C+1):
                poly_log[x]+=poly[x]*cnt[c]%mod
                poly_log[x]%=mod
    return 1
    poly=exp(poly_log)
    retu=poly[C]*fact[C]%mod
    return retu

for d in range(K):
    ans+=solve(math.gcd(K,d))
    ans%=mod
ans*=pow(K,mod-2,mod)
ans%=mod
print(ans)

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結果

テストケース

ソースコード