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.IOException;
import java.io.PrintWriter;
import java.util.Scanner;

public class A {

    static void solve() throws IOException {
        long a = in.nextLong();
        long b = in.nextLong();
        long m = 1000000007;
        long t = ( a + b * ( a * ( a + 1 ) / 2 % m ) ) % m;
        out.println( b * ( b - 1 ) / 2 % m * t % m );
    }

    static Scanner in;
//    static StreamTokenizer in;
    static PrintWriter out;

//    static int nextInt() throws IOException {
//        in.nextToken();
//        return ( int ) in.nval;
//    }

    public static void main( String[] args ) throws IOException {
        in = new Scanner( System.in );
//        in = new StreamTokenizer( new InputStreamReader( System.in ) );
        out = new PrintWriter( System.out );
        solve();
        out.close();
    }
}
