Little Elephant and Triangle

3000ms

262144K

Description:

The Little Elephant is playing with the Cartesian coordinates' system. Most of all he likes playing with integer points. The Little Elephant defines an integer point as a pair of integers (x; y), such that 0 ≤ x ≤ w and 0 ≤ y ≤ h. Thus, the Little Elephant knows only (w + 1)·(h + 1) distinct integer points.

The Little Elephant wants to paint a triangle with vertexes at integer points, the triangle's area must be a positive integer. For that, he needs to find the number of groups of three points that form such triangle. At that, the order of points in a group matters, that is, the group of three points (0;0), (0;2), (2;2) isn't equal to the group (0;2), (0;0), (2;2).

Help the Little Elephant to find the number of groups of three integer points that form a nondegenerate triangle with integer area.

Input:

A single line contains two integers w and h (1 ≤ w, h ≤ 4000).

Output:

In a single output line print an integer — the remainder of dividing the answer to the problem by 1000000007 (10⁹ + 7).

Sample Input:

2 1

Sample Output:

Sample Input:

2 2

Sample Output:

Informação

Provedor Codeforces

Código CF220D