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.*;
public class Test {
    public static int div = (int) (1e9 + 7 + 1) / 2;
    public static int mod = (int) 1e9 + 7;
    public static int sum(int n) {
        return (int) ((long)n * (n + 1) % mod * div % mod);
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt();
        int b = sc.nextInt();
        long ans = 0;
        ans = (long) b * sum(b - 1) % mod * sum(a) % mod;
        ans = (ans + (long) a * sum(b - 1)) % mod;
        System.out.println((int) ans);
    }
}