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 Class{

    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        BigInteger bi1, bi2, bi3, bi4, bi5, bi6, bi7, bi8, bi9;  
        long a = Long.parseLong(st.nextToken());
        long b = Long.parseLong(st.nextToken());
        bi1 = new BigInteger(a+"");
        bi2 = new BigInteger(b+"");
        bi3 = bi1.multiply(bi2);
        bi4 = bi1.multiply(bi2.add(bi3).add(new BigInteger(2+"")));
        bi5 = bi4.multiply(bi2.subtract(new BigInteger(1+""))).multiply(bi2);
        bi6 = bi5.divide(new BigInteger(4+""));
        System.out.print(bi6.mod(new BigInteger(1000000007+"")));
    }
    
    
    static class Pair{
        long start;
        long end;
        
        public Pair(long start, long end){
            this.start = start;
            this.end = end;
        }
        
        public int hashCode() {
            return (int)(this.start + this.end);
        }
        
        public boolean equals(Object p){
            if(((Pair)p).start==this.start && ((Pair)p).end==this.end)return true;
            return false;
        }
    }
}