結果

問題 No.886 Direct
ユーザー vwxyz
提出日時 2021-09-30 09:51:42
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 3,697 ms / 4,000 ms
コード長 4,749 bytes
コンパイル時間 247 ms
コンパイル使用メモリ 82,428 KB
実行使用メモリ 296,728 KB
最終ジャッジ日時 2024-07-17 13:10:03
合計ジャッジ時間 40,310 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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ファイルパターン 結果
sample AC * 4
other AC * 32
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ソースコード

diff #
プレゼンテーションモードにする

import math
from collections import defaultdict
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_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 Fact(self,N):
        if N<0:
            return 0
        return self.factorial[N]*pow(self.p,self.cnt[N],self.mod)%self.mod
    def Fact_Inve(self,N):
        if 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.factorial_inve[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=map(int,input().split())
cnt=[0]*(max(H,W)+1)
mod=10**9+7
MD=MOD(mod)
MD.Build_Fact(max(H,W)+1)
P=Prime(max(H,W)+1)
for g in range(1,max(H,W)+1):
    n_H,c_H=divmod(H,g)
    n_W,c_W=divmod(W,g)
    cnt[g]=((MD.Comb(n_H,2)*(g-c_H)+MD.Comb(n_H+1,2)*c_H)*(MD.Comb(n_W,2)*(g-c_W)+MD.Comb(n_W+1,2)*c_W)*2%mod)
    cnt[g]+=H*(MD.Comb(n_W,2)*(g-c_W)+MD.Comb(n_W+1,2)*c_W)+W*(MD.Comb(n_H,2)*(g-c_H)+MD.Comb(n_H+1,2)*c_H)
ans=0
for g in range(1,max(H,W)+1):
    ans+=P.Mebius(g)*cnt[g]
    ans%=mod
print(ans)
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