結果

問題 No.377 背景パターン
コンテスト
ユーザー vwxyz
提出日時 2021-08-17 01:21:42
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
TLE  
実行時間 -
コード長 5,460 bytes
コンパイル時間 107 ms
コンパイル使用メモリ 13,184 KB
実行使用メモリ 13,824 KB
最終ジャッジ日時 2024-10-10 00:15:19
合計ジャッジ時間 8,252 ms
ジャッジサーバーID
（参考情報） 		judge4 / 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 * 5
other AC * 11 TLE * 1 -- * 2
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 # 

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

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=1):
        self.p=p
        self.e=e
        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]
        self.cnt=[0]*(N+1)
        for i in range(1,N+1):
            ii=i
            self.cnt[i]=self.cnt[i-1]
            while ii%self.p==0:
                ii//=self.p
                self.cnt[i]+=1
            self.factorial.append((self.factorial[-1]*ii)%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):
            ii=i+1
            while ii%self.p==0:
                ii//=self.p
            self.factorial_inv[i]=(self.factorial_inv[i+1]*ii)%self.mod

    def Fact(self,N):
        return self.factorial[N]*pow(self.p,self.cnt[N],self.mod)%self.mod

    def Fact_Inv(self,N):
        if self.cnt[N]:
            return None
        return self.factorial_inv[N]

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

H,W,K=map(int,readline().split())
P=Prime(10**5)
dct_H,dct_W={},{}
divisors_H,divisors_W=sorted(P.Divisors(H)),sorted(P.Divisors(W))
for d in divisors_H:
    dct_H[d]=H//d
for d in divisors_W:
    dct_W[d]=W//d
for p in P.Factorize(H):
    for d in divisors_H:
        if d%p==0:
            dct_H[d//p]-=dct_H[d]
for p in P.Factorize(W):
    for d in divisors_W:
        if d%p==0:
            dct_W[d//p]-=dct_W[d]
ans=0
mod=10**9+7
MD=MOD(mod)
for d_H in divisors_H:
    for d_W in divisors_W:
        g=GCD(H//d_H,W//d_W)
        ans+=dct_H[d_H]*dct_W[d_W]*pow(K,d_H*d_W*g,mod)
        ans%=mod
ans*=MD.Pow(H*W,-1)
ans%=mod
print(ans)
0