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.*;
import java.io.*;
import java.math.*;

public class C {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		BigInteger a = sc.nextBigInteger();
		BigInteger b = sc.nextBigInteger();
		BigInteger TWO = BigInteger.valueOf(2);
		BigInteger MOD = BigInteger.valueOf(1000000007);
		BigInteger bbmin1 = b.multiply(b.subtract(BigInteger.ONE));
		BigInteger x = bbmin1.multiply(b.add(BigInteger.ONE));
		BigInteger y = a.subtract(BigInteger.ONE).multiply(bbmin1).multiply(b).divide(TWO);
		BigInteger res = x.add(y).multiply(a).divide(TWO).remainder(MOD);
		System.out.println(res);
	}
}