Dreamoon and Sums

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 and , where k is some integer number in range [1, a].

By we denote the quotient of integer division of x and y. By 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?

The single line of the input contains two integers a, b (1 ≤ a, b ≤ 10⁷).

Print a single integer representing the answer modulo 1 000 000 007 (10⁹ + 7).

1 1

0

2 2

8

 Note

For the first sample, there are no nice integers because  is always zero.
For the second sample, the set of nice integers is {3, 5}.