Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].

By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.

The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?

Input

The single line of the input contains two integers a, b (1 ≤ a, b ≤ 107).

Output

Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).

Examples

Input

1 1


Output

0


Input

2 2


Output

8

Note

For the first sample, there are no nice integers because <image> is always zero.

For the second sample, the set of nice integers is {3, 5}.
import java.util.*;
import java.lang.*;
import java.io.*;

public class Main
{
    public static void main (String[] args) throws Exception
    {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        while(sc.hasNext()) {
            long a = sc.nextLong();
            long b = sc.nextLong();
            long mod = 1000000007;
            if(b == 1) { out.println(0); }
            else {
                long ta = a*(a+1)/2;
                long tb = b*(b-1)/2;
                ta %= mod; tb %= mod;
                long c = (b*ta+a) % mod;
                long ans = (c*tb) % mod;
                out.println(ans);
            }
        }
        sc.close();
        out.close();
    }
}