P3704 [SDOI2017]数字表格

 

#include <iostream>
#include <cstdio>
#include <queue>
#include <algorithm>
#include <cmath>
#include <cstring>
#define inf 2147483647
#define N 1000010
#define mod 1000000007
#define p(a) putchar(a)
#define For(i,a,b) for(long long i=a;i<=b;++i)
//by war
//2020.8.7
using namespace std;
long long T,n,m,cnt,ans,a,b,c,d,k;
long long prime[N],mu[N],f[N],F[N],g[N],prod[N];
bool vis[N];
void in(long long &x){
    long long y=1;char c=getchar();x=0;
    while(c<'0'||c>'9'){if(c=='-')y=-1;c=getchar();}
    while(c<='9'&&c>='0'){ x=(x<<1)+(x<<3)+c-'0';c=getchar();}
    x*=y;
}
void o(long long x){
    if(x<0){p('-');x=-x;}
    if(x>9)o(x/10);
    p(x%10+'0');
}

long long ksm(long long a,long long b){
    long long r=1;
    while(b>0){
        if(b&1) r=r*a%mod;
        a=a*a%mod;
        b>>=1;
    }
    return r;
}

void Euler(long long n){
    mu[1]=1;
    f[0]=0;f[1]=F[0]=F[1]=prod[0]=g[0]=g[1]=1;
    For(i,2,n){
        if(!vis[i]) prime[++cnt]=i,mu[i]=-1;
        for(long long j=1;j<=cnt&&i*prime[j]<=n;j++){
            vis[i*prime[j]]=1;
            if(i%prime[j]==0){
                mu[i*prime[j]]=0;
                break;
            }
            mu[i*prime[j]]=-mu[i];
        }
        F[i]=1;
        f[i]=(f[i-1]+f[i-2])%mod;
        g[i]=ksm(f[i],mod-2);
    }
    For(i,1,n){
        if(mu[i]!=0){
            for(long long j=i;j<=n;j+=i)
                F[j]=F[j]*(mu[i]==1?f[j/i]:g[j/i])%mod;
        }
        prod[i]=prod[i-1]*F[i]%mod;
    }
}

long long solve(long long n,long long m){
    long long r=1,k;
    for(long long i=1,j;i<=n;i=j+1){
        j=min(n/(n/i),m/(m/i));
        k=prod[j]*ksm(prod[i-1],mod-2)%mod;
        r=r*ksm(k,(n/i)*(m/i)%(mod-1))%mod;
    }
    return r;
}

signed main(){
    Euler(1e6);
    in(T);
    while(T--){
        in(n);in(m);
        if(n>m) swap(n,m);
        ans=solve(n,m);
        o(ans);p('
');
    }
    return 0;
}

//这场比赛我去现场打过，所以我对这题很有印象，当时只会暴力...