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.ArrayList;
import java.util.Scanner;

public class DreamoonandSums {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int a = in.nextInt();
		long b = in.nextLong();
		long ans = 0;

		long mod = 1000000007;
		long step = 0;
		if (b % 2 == 0) {
			long y = b / 2;
			ans = (b - 1) % mod * (b + 1) % mod * y % mod;

			step = (b - 1) % mod * y % mod * b % mod;

		} else {
			long y = (b - 1) / 2;
			step = y % mod * b % mod * b % mod;
			ans = y % mod * (b + 1) % mod * b % mod;

		}
		ans %= mod;
		step %= mod;
		long p = ans;
		for (int i = 2; i <= a; i++) {
			p += step;
			p %= mod;
			ans += p;
			ans %= mod;
		}

		System.out.println(ans);

	}

}
