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.*;
import java.util.*;

public class cf272C {
	public static void main(String[] args) throws Exception {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		// BufferedReader in = new BufferedReader(new FileReader("cf272C.in"));

		String str = in.readLine();
		long a = Long.parseLong(str.substring(0, str.indexOf(" ")));
		long b = Long.parseLong(str.substring(str.indexOf(" ") + 1));

		long mod = 1000000007;
		long ans = a * (a + 1) / 2;
		ans %= mod;
		ans *= b;
		ans %= mod;
		ans = (ans + a) % mod;
		long ans2 = (b - 1) * b / 2;
		ans2 %= mod;
		System.out.println((ans * ans2) % mod);
	}
}