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.*;
public class A {
    public static PrintStream out = System.out;
    public static InputReader in = new InputReader(System.in);
    public static void main(String args[]) {
        long a = in.nextLong();
        long b = in.nextLong();
        long MOD = (long) 1e9 + 7;
        long c = b * (b - 1) / 2 % MOD;
        long d = a * (a + 1) / 2 % MOD;
        d = (d * b + a) % MOD;
        out.println(c * d % MOD);
    }
}
class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
    public InputReader(InputStream stream) {
	reader = new BufferedReader(new InputStreamReader(stream), 32768);
	tokenizer = null;
    }
    public String next() {
	while (tokenizer == null || !tokenizer.hasMoreTokens()) {
	    try {
		tokenizer = new StringTokenizer(reader.readLine());
	    } catch (IOException e) {
		throw new RuntimeException(e);
	    }
	}
	return tokenizer.nextToken();
    }
    public double nextDouble() {
	return Double.parseDouble(next());
    }
    public long nextLong() {
	return Long.parseLong(next());
    }
    public int nextInt() {
	return Integer.parseInt(next());
    }
}
