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;
import java.math.BigDecimal;

public class CF272_1_A {
  public static void main(String[] args) throws Exception {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    String input = br.readLine();
    String[] ss = input.split(" ");

    int a = Integer.parseInt(ss[0]);
    int b = Integer.parseInt(ss[1]);

    int divide = 1000000007;

    BigDecimal abig = new BigDecimal(a);
    BigDecimal bbig = new BigDecimal(b);
    BigDecimal b1 = bbig.multiply(bbig.subtract(new BigDecimal(1))).divide(new BigDecimal(2));
    BigDecimal b2 = abig.multiply(abig.add(new BigDecimal(1)).multiply(bbig).divide(new BigDecimal(2))).add(abig);
    BigDecimal s = b1.multiply(b2).divideAndRemainder(new BigDecimal(divide))[1];
    System.out.println(s.intValue());
  }
}
