Given is a grid consisting of r rows by c columns of grid points.

Count the number of ways in which it is possible to draw a strictly concave quadrilateral with vertices in four of the given grid points.

(A quadrilateral is strictly concave if and only if one of its two diagonals contains a point that is strictly outside the quadrilateral. Shifted and/or rotated copies of the same quadrilateral count as distinct ways of drawing it.)

Input specification

The input has a single line with the two integers r and c.

You may assume that the total number of grid points is at most 3000.

Output specification

Output a single line with a single integer: the number of concave quadrilaterals with vertices on the grid.

Examples

2 10

0

3 3

24