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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Test {

	public static void main(String[] agrs) throws IOException {

		BufferedReader reader = new BufferedReader(new InputStreamReader(
				System.in));
		String[] strings = reader.readLine().split(" ");
		long a = Integer.valueOf(strings[0]);
		long b = Integer.valueOf(strings[1]);
		final int MOD = 1000000007;
		long calculateA = ((((((a * (a + 1) / 2) % MOD) * b) % MOD) + a) % MOD);
		long calculateB = ((b * (b - 1) / 2) % MOD);
		System.out.println(((calculateA * calculateB) % MOD) % MOD);
	}
}
