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 Main {
	private void a(){
		Scanner sc = new Scanner(System.in);
		while(sc.hasNext()){
			int n = sc.nextInt(), m = sc.nextInt();
			int f = -1, lowBound = n + 1 >> 1;
			for(int i = m; i <= n; i+=m)
				if(i >= lowBound){
					f = i;		break;
				}
			System.out.println(f);
		}
	}
	
	private void c(){
		long mod = 1000000007;
		Scanner sc = new Scanner(System.in);
		while(sc.hasNext()){
			long a = sc.nextLong(), b = sc.nextLong();
			long ans1 = ( (((a*(a+1)/2)%mod) *b)%mod + a) % mod,
				 ans2 =( ans1 * ((b*(b-1)/2) % mod)) % mod;
			System.out.println(ans2);
		}
	}
	
	public static void main(String[] args) {
		new Main().c();
	}
}
