CLTNGL_tester.java

import java.util.*;
import java.io.*;
 
class triangle_grid{
static Vector<Integer>prime = new Vector<>();
static boolean is_composite[]=new boolean[1000001];
static long phi1[]=new long[1000001];
static long phi2[]=new long[1000001];
static int M=1000000007;
public static long power(long x, long y, long m)
{
    if (y == 0)
        return 1;
    long p = power(x, y / 2, m) % m;
    p = (p * p) % m;
 
    return (y % 2 == 0) ? p : (x * p) % m;
}
public static long sum(long n){
   long x=(long)n*(n+1)/2;
    return x%M; 
}
public static long mul(long a,long b,long c,long d)
{
    long ans=a;
    ans=(ans*b)%M;
    ans=(ans*c)%M;
    ans=(ans*d)%M;
    return ans;
}
public static void sieve (int n) {
    for (int i = 2; i < n; ++i) {
        if (!is_composite[i]) {
            prime.add(i);
            phi1[i] = i - 1; 
            phi2[i] =(long) i*i - 1;
        }
        for (int j = 0; j < prime.size () && (i*prime.get(j))<=n; ++j) {
            is_composite[i * prime.get(j)] = true;
            if (i % prime.get(j) == 0) {
                phi1[i * prime.get(j)] = phi1[i] * prime.get(j); 
                phi2[i * prime.get(j)] = phi2[i] * prime.get(j)*prime.get(j); 
                break;
            } else {
                phi1[i * prime.get(j)] = phi1[i] * phi1[prime.get(j)];
                phi2[i * prime.get(j)] = phi2[i] * phi2[prime.get(j)];
            }
        }
    }
}
    public static void main(String[] args)throws IOException {
        Scanner in=new Scanner(System.in);
        long n=in.nextInt();
        long m=in.nextInt();
        sieve((int)n);
        int i,j;
        phi1[1]=phi2[1]=1;
        long x=n-1;
        long y=m-1;
        long p,q,count,sum1,sum2,c1,c2,c3,c4,num,den,mmif,ans;
        count=sum1=sum2=c1=c2=c3=c4=num=den=0;
        for(i=1;i<=x;i++)
        {
            count=0;
            p=x/i;
            q=y/i;
            count=(count+mul(n,m,p,q))%M;
            count=(count-mul(n,i,p,sum(q))+M)%M;
            count=(count-mul(i,m,sum(p),q)+M)%M;
            count=(count+mul(i,i,sum(p),sum(q)))%M;
            sum1=(sum1+(count*(phi1[i]%M))%M)%M;
            sum2=(sum2+(count*(phi2[i]%M))%M)%M;
        }
        for(i=1;i<=x;i++)
        {
            c1=(c1+((n-i)*i)%M)%M;
            c3=(c3+mul((n-i),1,i,i))%M;
        }
        for(i=1;i<=y;i++)
        {
            c2=(c2+((m-i)*i)%M)%M;
            c4=(c4+mul((m-i),1,i,i))%M;
        }
        sum1=(sum1*4)%M;
        sum1=(sum1+mul(2,1,m,c1))%M;
        sum1=(sum1+mul(2,1,n,c2))%M;
        sum2=(sum2*4)%M;
        sum2=(sum2+mul(2,1,m,c3))%M;
        sum2=(sum2+mul(2,1,n,c4))%M;
        num=(num+mul(3,n,m,sum1))%M;
        num=(num-mul(1,1,6,sum2)+M)%M;
        x=(n*n)%M;
        y=(m*m)%M;
        den=(den+mul(n,m,x,y))%M;
        den=(den-mul(3,1,1,sum1)+M)%M;
        den=(den-mul(1,1,n,m)+M)%M;
        mmif=power(den,M-2,M);
        ans=(num*mmif)%M;
        System.out.println(ans);
    }
}