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.IOException;
import java.io.InputStreamReader;

public class DreamoonAndSums {

    public static long getGaussionSumation(long a) {
        return (a * (a + 1)) / 2;
    }

    public static void main(String[] args) throws IOException {

        BufferedReader reader = new BufferedReader(new InputStreamReader(
                System.in));
        String[] strings = reader.readLine().split(" ");
        long a = Long.valueOf(strings[0]);
        long b = Long.valueOf(strings[1]);
        final int MOD = 1000000007;
        long calcualtionOfA = (((getGaussionSumation(a) % MOD) * b) % MOD + a)
                % MOD;
        long calculationOfB = (b * (b - 1)) / 2 % MOD;
        System.out.println((calcualtionOfA * calculationOfB) % MOD);
    }
}
