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.BufferedReader;
import java.io.InputStreamReader;

public class R272D1A {

    private static final String LNSP = System.getProperty("line.separator");

    public static void main(String args[] ) throws Exception {
        StringBuilder cout = new StringBuilder();

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String line;
        String[] words;
        line = br.readLine();
        words = line.split(" ");
        long a = Long.parseLong(words[0]);
        long b = Long.parseLong(words[1]);

        long ret = 0L;
        final long div = 1000000007L;
        ret = ((a+1) * a / 2);
        ret %= div;
        ret *= b;
        ret %= div;
        ret += a;
        ret %= div;
        long argb = (b * (b-1) / 2) % div;
        ret *= argb;
        ret %= div;
        cout.append(ret);
        cout.append(LNSP);
        System.out.print(cout);
    }

}
