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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {
    
    static int MODULO = 1000000007;
    
    public static void main(String argc[]) throws Exception {
        int i,j,k;
        int y;
        
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        long a = Integer.parseInt(st.nextToken());
        int b = Integer.parseInt(st.nextToken());
        long score = 0;
        long sum = 0;
        
        for (y=1;y<b;y++) {
            score = a*(a+1)/2;
            score %= MODULO;
            score *= y;
            score %= MODULO;
            score *= b;
            score %= MODULO;
            score += y*a;
            score %= MODULO;
            sum += score;
            sum %= MODULO;
        }
        
        System.out.println(sum);
        
    }
    
}
