結果

問題 No.575 n! / m / m / m...
ユーザー vwxyz
提出日時 2021-08-17 03:16:09
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
AC  
実行時間 364 ms / 2,000 ms
コード長 3,826 bytes
コンパイル時間 327 ms
コンパイル使用メモリ 13,056 KB
実行使用メモリ 25,600 KB
最終ジャッジ日時 2024-10-10 01:51:57
合計ジャッジ時間 7,537 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

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
        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 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
N,M=map(int,readline().split())
if N<=1000:
    ans=1
    for i in range(1,N+1):
        ans*=i
    while ans%M==0:
        ans//=M
    d=len(str(ans))-1
    p=ans/pow(10,d)
else:
    ans_log=N*(math.log10(N)-math.log10(math.e))+math.log10(2*math.pi*N)/2
    P=Prime(10**6)
    cnt=1<<60
    MM=M
    for p in P.primes:
        if M%p==0:
            cnt_M=0
            while MM%p==0:
                cnt_M+=1
                MM//=p
            NN=N
            cnt_N=0
            while NN:
                NN//=p
                cnt_N+=NN
            cnt=min(cnt,cnt_N//cnt_M)
    if MM!=1:
        p=MM
        cnt_M=1
        NN=N
        cnt_N=0
        while NN:
            NN//=p
            cnt_N+=NN
        cnt=min(cnt,cnt_N//cnt_M)
    ans_log-=math.log10(M)*cnt
    d=int(ans_log)
    p=ans_log-d
    p=10**p
print(p,"e",d,sep="")
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