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 {

	static Scanner sc = new Scanner(System.in);
	static final int MOD = 1_000_000_007;

	public static void main(String[] args) {
		long A = sc.nextInt();
		long B = sc.nextInt();
		if (B == 1) {
			System.out.println(0);
			return;
		}
		long ans1 = B * (B - 1) / 2;
		ans1 %= MOD;
		long ans2 = A * (A + 1) / 2;
		ans2 %= MOD;
		ans2 *= B;
		ans2 += A;
		ans2 %= MOD;
		System.out.println((ans1 * ans2) % MOD);
	}

}
