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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeSet;

import javax.swing.text.html.HTMLDocument.Iterator;

public class HelloWorld {
    
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        long a = in.nextLong();
        long b = in.nextLong();
        long sum = 0;
        long mid = 1000000007;
        long sum1 = b *(b - 1) / 2;
        sum1 = sum1 % mid;
        long sum2 = (a * (a + 1) / 2 ) % mid;
        sum2 =( sum2 * b + a) % mid;
        long result = (sum1 * sum2) % mid;
        System.out.println(result);
    }
}