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 main1 {
	static long MOD = 1000000007;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
	
		long a = sc.nextLong();
		long b = sc.nextLong();

		long ans = 0;
		for (int i = 1; i <= a; i++) {
			
			long sum = (long)(((1d + (b - 1)) / 2d) * (b - 1)) % MOD;
			long sum2 = b * sum;
			sum2 = sum2 % MOD;
			sum2 *= i;
			sum2 = sum2 % MOD;
			
			ans += sum + sum2;
			ans = ans % MOD;
		}
		
		System.out.println(ans);
	}
}
