結果

問題 No.8038 フィボナッチ数列の周期
コンテスト
ユーザー vwxyz
提出日時 2021-10-21 03:15:09
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 960 ms / 3,000 ms
コード長 4,872 bytes
コンパイル時間 300 ms
コンパイル使用メモリ 81,920 KB
実行使用メモリ 225,920 KB
最終ジャッジ日時 2024-09-20 06:52:10
合計ジャッジ時間 21,337 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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ファイルパターン 結果
other AC * 25
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ソースコード

diff # 

import bisect
import copy
import decimal
import fractions
import functools
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
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines

class Prime:
    def __init__(self,N):
        assert N<=10**8
        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
        factors=defaultdict(int)
        if N<=len(self.smallest_prime_factor)-1:
            while N!=1:
                factors[self.smallest_prime_factor[N]]+=1
                N//=self.smallest_prime_factor[N]
        else:
            for p in self.primes:
                while N%p==0:
                    N//=p
                    factors[p]+=1
                if N<p*p:
                    if N!=1:
                        factors[N]+=1
                    break
                if N<=len(self.smallest_prime_factor)-1:
                    while N!=1:
                        factors[self.smallest_prime_factor[N]]+=1
                        N//=self.smallest_prime_factor[N]
                    break
            else:
                if N!=1:
                    factors[N]+=1
        return factors

    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 Mebius(self,N):
        fact=self.Factorize(N)
        for e in fact.values():
            if e>=2:
                return 0
        else:
            if len(fact)%2==0:
                return 1
            else:
                return -1

def Bostan_Mori(poly_nume,poly_deno,N,mod=0,fft=False,ntt=False):
    if ntt:
        convolve=NTT
    elif fft:
        convolve=FFT
    else:
        def convolve(poly_nume,poly_deno):
            conv=[0]*(len(poly_nume)+len(poly_deno)-1)
            for i in range(len(poly_nume)):
                for j in range(len(poly_deno)):
                    conv[i+j]+=poly_nume[i]*poly_deno[j]
            if mod:
                for i in range(len(conv)):
                    conv[i]%=mod
            return conv
    while N:
        poly_deno_=[-x if i%2 else x for i,x in enumerate(poly_deno)]
        if N%2:
            poly_nume=convolve(poly_nume,poly_deno_)[1::2]
        else:
            poly_nume=convolve(poly_nume,poly_deno_)[::2]
        poly_deno=convolve(poly_deno,poly_deno_)[::2]
        if fft and mod:
            for i in range(len(poly_nume)):
                poly_nume[i]%=mod
            for i in range(len(poly_deno)):
                poly_deno[i]%=mod
        N//=2
    return poly_nume[0]

N=int(readline())
lcm=defaultdict(int)
mod=10**9+7
Pr=Prime(10**7)
for i in range(N):
    P,K=map(int,readline().split())
    if P==2:
        period=3
    elif P==5:
        period=20
    else:
        if P%5 in (1,4):
            period=P-1
        else:
            period=2*P+2
        for p,e in Pr.Factorize(period).items():
            for _ in range(e):
                a=Bostan_Mori([0,1],[1,-1,-1],period//p,mod=P)
                b=Bostan_Mori([0,1],[1,-1,-1],period//p+1,mod=P)
                if (a,b)==(0,1):
                    period//=p
                else:
                    break
    fact=defaultdict(int)
    for p,e in Pr.Factorize(period).items():
        fact[p]+=e
    for p,e in Pr.Factorize(P).items():
        fact[p]+=e*(K-1)
    for p,e in fact.items():
        lcm[p]=max(lcm[p],e)
ans=1
for p,e in lcm.items():
    ans*=pow(p,e,mod)
    ans%=mod
print(ans)
0