Picnic Rhombi

Time limit2sMemory limit128 MB

Summary

Count every rhombus whose four vertices sit on lattice points of an N by M grid of unit squares.

Level: Hard8 of 10
Topics: Combinatorics, Geometry, Math, Number theory
Solved: No attempts yet

Problem

A group of people on a picnic divides a wide lawn into an N x M grid. The grid consists of unit squares of size 1 x 1.

You want to draw rhombi on this grid. All four vertices of a rhombus must lie on vertices of the unit squares, that is, on lattice points of the grid. Squares are included because all four of their sides have the same length.

Given N and M, find the number of different rhombi that can be drawn. Two rhombi are different if their sets of vertices differ by at least one point.

Input

The first line contains two integers N and M.

Output

Print the number of different rhombi that can be drawn.

Constraints

1 <= N, M <= 100

Examples3

Example 1
Input
```
2 2
```
Expected output
```
6
```
Example 2
Input
```
1 6
```
Expected output
```
6
```
Example 3
Input
```
6 8
```
Expected output
```
527
```