結果

問題 No.2313 Product of Subsequence (hard)
ユーザー vwxyzvwxyz
提出日時 2023-11-28 22:32:52
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,888 ms / 4,000 ms
コード長 4,444 bytes
コンパイル時間 440 ms
コンパイル使用メモリ 82,560 KB
実行使用メモリ 182,388 KB
最終ジャッジ日時 2024-09-26 13:11:35
合計ジャッジ時間 21,924 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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 AC 150 ms
89,472 KB
testcase_01 AC 143 ms
89,600 KB
testcase_02 AC 147 ms
89,600 KB
testcase_03 AC 155 ms
90,496 KB
testcase_04 AC 160 ms
90,496 KB
testcase_05 AC 184 ms
90,880 KB
testcase_06 AC 155 ms
90,496 KB
testcase_07 AC 164 ms
90,368 KB
testcase_08 AC 336 ms
147,228 KB
testcase_09 AC 248 ms
113,280 KB
testcase_10 AC 384 ms
175,592 KB
testcase_11 AC 238 ms
116,608 KB
testcase_12 AC 388 ms
177,036 KB
testcase_13 AC 1,888 ms
182,256 KB
testcase_14 AC 1,742 ms
182,124 KB
testcase_15 AC 1,666 ms
182,128 KB
testcase_16 AC 1,823 ms
182,388 KB
testcase_17 AC 1,541 ms
182,260 KB
testcase_18 AC 1,568 ms
182,136 KB
testcase_19 AC 1,525 ms
182,264 KB
testcase_20 AC 1,554 ms
182,252 KB
testcase_21 AC 150 ms
89,728 KB
testcase_22 AC 146 ms
89,344 KB
testcase_23 AC 147 ms
89,472 KB
testcase_24 AC 148 ms
89,728 KB
testcase_25 AC 373 ms
175,820 KB
testcase_26 AC 278 ms
129,092 KB
testcase_27 AC 1,053 ms
165,532 KB
testcase_28 AC 426 ms
181,608 KB
testcase_29 AC 432 ms
182,004 KB
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ソースコード

diff # 

import bisect
import copy
import decimal
import fractions
import heapq
import itertools
import math
import random
import sys
import time
from collections import Counter,deque,defaultdict
from functools import lru_cache,reduce
from heapq import heappush,heappop,heapify,heappushpop,_heappop_max,_heapify_max
def _heappush_max(heap,item):
    heap.append(item)
    heapq._siftdown_max(heap, 0, len(heap)-1)
def _heappushpop_max(heap, item):
    if heap and item < heap[0]:
        item, heap[0] = heap[0], item
        heapq._siftup_max(heap, 0)
    return item
from math import gcd as GCD
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines
write=sys.stdout.write
#import pypyjit
#pypyjit.set_param('max_unroll_recursion=-1')
#sys.set_int_max_str_digits(10**9)

def Divisors(N):
    divisors=[]
    for i in range(1,N+1):
        if i**2>=N:
            break
        elif N%i==0:
            divisors.append(i)
    if i**2==N:
        divisors+=[i]+[N//i for i in divisors[::-1]]
    else:
        divisors+=[N//i for i in divisors[::-1]]
    return divisors

def Extended_Euclid(n,m):
    stack=[]
    while m:
        stack.append((n,m))
        n,m=m,n%m
    if n>=0:
        x,y=1,0
    else:
        x,y=-1,0
    for i in range(len(stack)-1,-1,-1):
        n,m=stack[i]
        x,y=y,x-(n//m)*y
    return x,y

class MOD:
    def __init__(self,p,e=None):
        self.p=p
        self.e=e
        if self.e==None:
            self.mod=self.p
        else:
            self.mod=self.p**self.e

    def Pow(self,a,n):
        a%=self.mod
        if n>=0:
            return pow(a,n,self.mod)
        else:
            #assert math.gcd(a,self.mod)==1
            x=Extended_Euclid(a,self.mod)[0]
            return pow(x,-n,self.mod)

    def Build_Fact(self,N):
        assert N>=0
        self.factorial=[1]
        if self.e==None:
            for i in range(1,N+1):
                self.factorial.append(self.factorial[-1]*i%self.mod)
        else:
            self.cnt=[0]*(N+1)
            for i in range(1,N+1):
                self.cnt[i]=self.cnt[i-1]
                ii=i
                while ii%self.p==0:
                    ii//=self.p
                    self.cnt[i]+=1
                self.factorial.append(self.factorial[-1]*ii%self.mod)
        self.factorial_inve=[None]*(N+1)
        self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1)
        for i in range(N-1,-1,-1):
            ii=i+1
            while ii%self.p==0:
                ii//=self.p
            self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod

    def Build_Inverse(self,N):
        self.inverse=[None]*(N+1)
        assert self.p>N
        self.inverse[1]=1
        for n in range(2,N+1):
            if n%self.p==0:
                continue
            a,b=divmod(self.mod,n)
            self.inverse[n]=(-a*self.inverse[b])%self.mod
    
    def Inverse(self,n):
        return self.inverse[n]

    def Fact(self,N):
        if N<0:
            return 0
        retu=self.factorial[N]
        if self.e!=None and self.cnt[N]:
            retu*=pow(self.p,self.cnt[N],self.mod)%self.mod
            retu%=self.mod
        return retu

    def Fact_Inve(self,N):
        if self.e!=None and self.cnt[N]:
            return None
        return self.factorial_inve[N]

    def Comb(self,N,K,divisible_count=False):
        if K<0 or K>N:
            return 0
        retu=self.factorial[N]*self.factorial_inve[K]%self.mod*self.factorial_inve[N-K]%self.mod
        if self.e!=None:
            cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K]
            if divisible_count:
                return retu,cnt
            else:
                retu*=pow(self.p,cnt,self.mod)
                retu%=self.mod
        return retu

N,K=map(int,readline().split())
A=list(map(int,readline().split()))
D=Divisors(K)
mod=998244353
MD=MOD(mod)
MD.Build_Fact(N)
dp=defaultdict(int)
C=defaultdict(int)
for a in A:
    C[GCD(a,K)]+=1
dp[1]=1
for a,cnt in C.items():
    prev=dp
    dp=defaultdict(int)
    for d in D:
        p=pow(2,cnt,mod)
        dd=d
        dp[dd]+=prev[d]
        p-=1
        for c in range(1,cnt+1):
            if dd!=GCD(dd*a,K):
                dd=GCD(dd*a,K)
                dp[dd]+=prev[d]*MD.Comb(cnt,c)%mod
                p-=MD.Comb(cnt,c)
                p%=mod
            else:
                dp[dd]+=prev[d]*p
                break
    for d in D:
        dp[d]%=mod
dp[1]-=1
ans=dp[K]
print(ans)
0