結果

問題 No.109 N! mod M
コンテスト
ユーザー vwxyz
提出日時 2021-08-03 03:05:12
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 296 ms / 5,000 ms
コード長 5,179 bytes
コンパイル時間 262 ms
コンパイル使用メモリ 82,048 KB
実行使用メモリ 90,368 KB
最終ジャッジ日時 2024-09-16 14:49:50
合計ジャッジ時間 2,823 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
other AC * 9
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ソースコード

diff #
raw source code 

import bisect
import copy
import decimal
import fractions
import heapq
import itertools
import math
import random
import sys
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, inf, modf
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines

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,mod):
        self.mod=mod
    
    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]
        for i in range(1,N+1):
            self.factorial.append((self.factorial[-1]*i)%self.mod)
        self.factorial_inv=[None]*(N+1)
        self.factorial_inv[-1]=self.Pow(self.factorial[-1],-1)
        for i in range(N-1,-1,-1):
            self.factorial_inv[i]=(self.factorial_inv[i+1]*(i+1))%self.mod
        return self.factorial_inv

    def Fact(self,N):
        return self.factorial[N]

    def Fact_Inv(self,N):
        return self.factorial_inv[N]

    def Comb(self,N,K):
        if K<0 or K>N:
            return 0
        s=self.factorial[N]
        s=(s*self.factorial_inv[K])%self.mod
        s=(s*self.factorial_inv[N-K])%self.mod
        return s

class Prime:
    def __init__(self,N):
        self.smallest_prime_factor=[None]*(N+1)
        for i in range(2,N+1,2):
            self.smallest_prime_factor[i]=2
        n=int(N**.5)+1
        for p in range(3,n,2):
            if self.smallest_prime_factor[p]==None:
                self.smallest_prime_factor[p]=p
                for i in range(p**2,N+1,2*p):
                    if self.smallest_prime_factor[i]==None:
                        self.smallest_prime_factor[i]=p
        for p in range(n,N+1):
            if self.smallest_prime_factor[p]==None:
                self.smallest_prime_factor[p]=p
        self.primes=[p for p in range(N+1) if p==self.smallest_prime_factor[p]]

    def Factorize(self,N):
        assert N>=1
        factorize=defaultdict(int)
        if N<=len(self.smallest_prime_factor)-1:
            while N!=1:
                factorize[self.smallest_prime_factor[N]]+=1
                N//=self.smallest_prime_factor[N]
        else:
            for p in self.primes:
                while N%p==0:
                    N//=p
                    factorize[p]+=1
                if N<p*p:
                    if N!=1:
                        factorize[N]+=1
                    break
                if N<=len(self.smallest_prime_factor)-1:
                    while N!=1:
                        factorize[self.smallest_prime_factor[N]]+=1
                        N//=self.smallest_prime_factor[N]
                    break
            else:
                if N!=1:
                    factorize[N]+=1
        return factorize

    def Divisors(self,N):
        assert N>0
        divisors=[1]
        for p,e in self.Factorize(N).items():
            A=[1]
            for _ in range(e):
                A.append(A[-1]*p)
            divisors=[i*j for i in divisors for j in A]
        return divisors

    def Is_Prime(self,N):
        return N==self.smallest_prime_factor[N]

    def Totient(self,N):
        for p in self.Factorize(N).keys():
            N*=p-1
            N//=p
        return N

def CRT(lst_r,lst_m):
    r,m=lst_r[0],lst_m[0]
    for r0,m0 in zip(lst_r[1:],lst_m[1:]):
        if (r0,m0)==(-1,0):
            r,m=-1,0
            break
        r0%=m0
        g=math.gcd(m,m0)
        l=LCM(m,m0)
        if r%g!=r0%g:
            r,m=-1,0
            break
        r,m=(r0+m0*(((r-r0)//g)*Extended_Euclid(m0//g,m//g)[0]%(m//g)))%l,l
    return r,m

def LCM(n,m):
    if n or m:
        return abs(n)*abs(m)//math.gcd(n,m)
    return 0

T=int(readline())
P=Prime(10**5)
for _ in range(T):
    N,M=map(int,readline().split())
    lst_r,lst_m=[],[]
    if M==1:
        ans=0
    else:
        for p,e in P.Factorize(M).items():
            m=p**e
            if m<=N:
                r=0
            elif e==1:
                r=1
                for i in range(N+1,p):
                    r*=i
                    r%=p
                r=(-1)*MOD(p).Pow(r,-1)%m
            else:
                r=1
                for i in range(1,N+1):
                    r*=i
                    r%=m
                    if r==0:
                        break
            lst_r.append(r)
            lst_m.append(m)
        ans,_=CRT(lst_r,lst_m)
    print(ans)
0