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 $\text{[math]}$ and $\text{[math]}$ , where k is some integer number in range [1, a].

By $\text{[math]}$ we denote the quotient of integer division of x and y. By $\text{[math]}$ 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).

Note

For the first sample, there are no nice integers because $\text{[math]}$ is always zero.

For the second sample, the set of nice integers is {3, 5}.

Dreamoon and Sums

Examples