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.Scanner;


public class C476 {
    public static void main (String [] args) {
        Scanner sc = new Scanner(System.in);
        
        long a = sc.nextLong();
        long b = sc.nextLong();
        
        long result1 = 0L;
        long result2 = 0L; 
        result2 = ((b*(b-1)) / 2)%1000000007;
        result1 = ((a*(a+1)) / 2)%1000000007;
        result1 = (result1 * b + a) % 1000000007;       
        result1 = result1 * (result2);
        System.out.println(result1 % 1000000007);
    }
}