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.io.*;
import java.lang.*;
import java.math.*;
public class A {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(bf.readLine());
        long a = Integer.parseInt(st.nextToken());
        long b = Integer.parseInt(st.nextToken());
        long ans = 0;
        for(int i=1; i<=a; i++) {
            ans += (1L*(1L*(b-1)*b)/2)%1000000007 * (1L*b*i%1000000007+1);
            ans %= 1000000007;
        }
        System.out.println(ans);
        // Scanner scan = new Scanner(System.in);
        // PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out)); 
        // int n = Integer.parseInt(bf.readLine());
        // StringTokenizer st = new StringTokenizer(bf.readLine());
        // int[] a = new int[n]; for(int i=0; i<n; i++) a[i] = Integer.parseInt(st.nextToken());
        // int n = Integer.parseInt(st.nextToken());
        // int n = scan.nextInt();
        
        // out.close(); System.exit(0);
    }
}