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.math.BigDecimal;
import java.math.BigInteger;  
import java.util.Scanner;  
import java.io.*;   
public class Main {  
    public static void main(String[] args) {  
        Scanner cin = new Scanner(System.in);  
        BigInteger a,b,ans1,ans2,ans;
        BigInteger MOD=BigInteger.valueOf(1000000007);
        while(cin.hasNext()){
        	a=cin.nextBigInteger();
        	b=cin.nextBigInteger();
        	ans1=(b.multiply(b.subtract(BigInteger.ONE)).divide(BigInteger.valueOf(2)));
        	ans2=a.multiply(b).multiply(a.add(BigInteger.ONE)).divide(BigInteger.valueOf(2)).add(a);
        	ans=ans1.multiply(ans2);
        	System.out.println(ans.mod(MOD));
        }
    }  
}