結果
| 問題 |
No.2959 Dolls' Tea Party
|
| コンテスト | |
| ユーザー |
 chineristAC
|
| 提出日時 | 2024-11-08 22:48:46 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 14,388 bytes |
| コンパイル時間 | 363 ms |
| コンパイル使用メモリ | 82,944 KB |
| 実行使用メモリ | 160,120 KB |
| 最終ジャッジ日時 | 2024-11-08 22:48:52 |
| 合計ジャッジ時間 | 6,302 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 2 TLE * 1 -- * 30 |
ソースコード
import sys,time
from itertools import permutations
from heapq import heappop,heappush
from collections import deque
import random
import bisect
from math import log,gcd
input = lambda :sys.stdin.readline().rstrip()
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
def mul(f,g):
res = [0 for i in range(len(f)+len(g)-1)]
for i in range(len(f)):
for j in range(len(g)):
res[i+j] += f[i] * g[j] % mod
res[i+j] %= mod
return res
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 BM(A,L):
"""
L+1項間漸化式を復元する
"""
assert len(A) >= 2 * L
# 初期化
C = [1] # 求める数列
B = [1] # 1つ前のCの状態を保存
L = 0 # Cの長さ-1
m = 1 # ポインタ？っぽいもの
b = 1 # 前回のdの値
for n in range(len(A)):
#d = C[0]*A[n] + C[1]*A[n-1] + ... + C[L]*A[n-L]
d = sum(C[i]*A[n-i] % mod for i in range(min(n,len(C)-1)+1))
if d == 0:
m += 1
elif 2 * L <= n:
T = C[:]
for i in range(len(B)):
if i+m < len(C):
C[i+m] -= d * pow(b,mod-2,mod) * B[i] % mod
C[i+m] %= mod
else:
C.append(-d * pow(b,mod-2,mod) * B[i] % mod)
L = n + 1 - L
B = T[:]
b = d
m = 1
# ③拡張しない場合
else:
for i in range(len(B)):
if i+m < len(C):
C[i+m] -= d * pow(b,mod-2,mod) * B[i] % mod
C[i+m] %= mod
else:
C.append(-d * pow(b,mod-2,mod) * B[i] % mod)
m += 1
return C
def bostan_mori(P,Q,N):
"""
[x^N]P(x)/Q(x)を求める
"""
d = len(Q) - 1
z = 1 << (2*d).bit_length()
iz = pow(z, _fft_mod - 2, _fft_mod)
while N:
"""
P(x)/Q(x) = P(x)Q(-x)/Q(x)Q(-x)
"""
P += [0] * (z-len(P))
Q += [0] * (z-len(Q))
_butterfly(P)
_butterfly(Q)
dft_t = Q.copy()
for i in range(0,z,2):
dft_t[i],dft_t[i^1] = dft_t[i^1],dft_t[i]
P = [a*b % mod for a,b in zip(P,dft_t)]
_butterfly_inv(P)
Q = [a*b % mod for a,b in zip(Q,dft_t)]
_butterfly_inv(Q)
P = [a * iz % mod for a in P][N&1::2]
Q = [a * iz % mod for a in Q][0::2]
N >>= 1
res = P[0] * pow(Q[0],mod-2,mod) % mod
return res
def taylor_shift(f,a):
"""
f(x+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))]
def poly_in_exp(f,M):
from collections import deque
"""
f(e^x)をM次まで求める
a_ne^nx->a_n 1/(1-nx)
"""
deq = deque([])
for i in range(len(f)):
deq.append(([[f[i]],[1,-i % mod]]))
while len(deq) > 1:
fq,fp = deq.popleft()
gq,gp = deq.popleft()
hp = convolution(fp,gp)
hq0 = convolution(fq,gp)
hq1 = convolution(gq,fp)
hq = [0] * max(len(hq0),len(hq1))
for i in range(len(hq0)):
hq[i] += hq0[i]
hq[i] %= mod
for i in range(len(hq1)):
hq[i] += hq1[i]
hq[i] %= mod
deq.append([hq,hp])
fq,fp = deq.popleft()
res = convolution(fq,inverse(fp,M+1))[:M+1]
for i in range(M+1):
res[i] *= g2[i]
res[i] %= mod
return res
def inverse(f,limit):
assert(f[0]!=0)
f += [0] * (limit-len(f))
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):
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 =convolve(res,h,2**i)
res = convolution(res,h)[:2**i]
return res[:limit]
def poly_pow_exp(f,k,limit):
l = len(f)
L = 1<<((l-1).bit_length())
n = L.bit_length()-1
f = f[:L]
f+=[0]*(L-len(f))
g = log(f,limit)
g = [(k * g[i]) % mod for i in range(len(g))]
h = exp(g,limit)
return h[:limit]
def poly_pow_rec(_f,k,limit):
f = _f[:] + [0] * (limit+1-len(_f))
g = [0] * limit
g[0] = 1
for n in range(limit-1):
if n+1 > (len(_f)-1) * k:
break
for i in range(n+1):
g[n+1] += g[i] * f[n-i+1] * (n-i+1) % mod
g[n+1] %= mod
g[n+1] = k * g[n+1] % mod
for i in range(1,n+1):
g[n+1] -= (n+1-i) * g[n+1-i] * f[i] % mod
g[n+1] %= mod
g[n+1] = g[n+1] * inv[n+1] % mod
#print(_f,g,k)
return g
def solve_brute(N,K,A):
memo = {}
def sub_solve(g):
if g in memo:
return memo[g]
block_size = K//g
f = [0] * (g+1)
f[0] = 1
for a in A:
a //= block_size
a = min(a,g)
ff = [g2[i] for i in range(a+1)]
f = mul(f,ff)[:g+1]
ans = f[g] * g1[g] % mod
memo[g] = ans
return ans
res = 0
for i in range(K):
res += sub_solve(gcd(i,K))
res %= mod
#print(memo)
res *= inv[K]
return res % mod
def solve_fast(N,K,A):
a_freq = [0] * (K+1)
for a in A:
a_freq[min(a,K)] += 1
memo = {}
def sub_solve(g):
if g in memo:
return memo[g]
block_size = K//g
tmp_freq = [0] * (g+1)
for a in range(1,K+1):
tmp_freq[a//block_size] += a_freq[a]
f = [0] * (g+1)
f[0] = 1
for a in range(1,g+1):
ff = [g2[i] for i in range(a+1)]
ff = poly_pow_exp(ff,tmp_freq[a],g+1)
f = convolution(f,ff)[:g+1]
ans = f[g] * g1[g] % mod
memo[g] = ans
return ans
res = 0
for i in range(K):
res += sub_solve(gcd(i,K))
res %= mod
#print(memo)
res *= inv[K]
return res % mod
def calc(K):
res = 0
for g in range(1,K+1):
if K % g == 0:
res += g**2
return res
N,K = mi()
A = li()
print(solve_fast(N,K,A))