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.math.BigInteger;

public class DreamoonSums476CTAKETWO
{
    public static void main(String[] args) 
    {
        // Set up scanner
        Scanner sc = new Scanner(System.in); 
        // System.out.println("Enter a");
        String a1 = sc.next();
        // System.out.println("Enter b");
        String b1 = sc.next();
        
        if (Integer.valueOf(b1) == 1)
        {
            System.out.println(0);
            return;
        }
        
        BigInteger a = new BigInteger(a1);
        BigInteger b = new BigInteger(b1);
        BigInteger two = new BigInteger("2");
        
        BigInteger tempone = a.multiply(b);
        BigInteger temptwo = tempone.add(b);
        BigInteger tempthree = temptwo.add(two);
        BigInteger tempfour = tempthree.multiply(a);
        BigInteger x = tempfour.divide(two);
        
        BigInteger tempfive = b.multiply(x);
        BigInteger tempsix = b.subtract(BigInteger.ONE);
        BigInteger tempseven = tempfive.multiply(tempsix);
        BigInteger tempeight = tempseven.divide(two);
        BigInteger answer = tempeight.mod(new BigInteger("1000000007"));
        System.out.println(answer);
    }
}