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.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class Test {
	public static void main(String[] args) {
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner(System.in);
		long a = in.nextInt();
		long b = in.nextInt();
		long result = 0;
		long mod = 1000000007; 
		long total = b* (b - 1)/2;
		total %= mod;
		 long other = a*(a + 1)/2;
		 other %= mod;
		 other *=b;
		 other %= mod;
		 other += a;
		 other %= mod;
		 total = total*other;
		 total %= mod;
		 out.println(total);
				 

		out.close();
	}
	
	
}
