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 {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in); 
		long enteroUno = in.nextInt();
		long enteroDos= in.nextInt();
		
		long resultado1 = (enteroDos*(enteroDos-1) /2) % 1000000007;
		long resultado2 = (enteroUno + ((enteroUno * (enteroUno + 1)/2) % 1000000007) * enteroDos) % 1000000007;
		long resultadofinal = (resultado1 * resultado2) % 1000000007;
		
		System.out.println(""+resultadofinal);
	 	}
}

	 	  			  		   	    	  		 	   	