City

Time limit1sMemory limit256 MB

Summary

Count the segments whose endpoints and midpoint are all grid points of an (n+1) by (m+1) lattice.

Level: Medium6 of 10
Topics: Math, Number theory, Geometry, Combinatorics
Solved: No attempts yet

Problem

Hi ICPCer, welcome to Xi'an.

Xi'an is a beautiful ancient city and the capital of the Zhou, Qin, Han, and Tang Dynasties. With a long history, the streets in Xi'an follow a grid pattern.

Attracted by the structure of the streets, Coach Pang wants to conduct his research on them. He draws an $n\times m$ grid on the board. The grid consists of $n+1$ vertical line segments and $m+1$ horizontal line segments. The vertical and horizontal line segments intersect at exactly $(n+1)\times(m+1)$ points, forming $n\times m$ unit squares. We call the $(n+1)\times (m+1)$ intersections grid points. Output the number of line segments $l$ (not only vertical or horizontal) satisfying the following three conditions:

The length is not zero.
Both endpoints of $l$ are grid points.
The midpoint of $l$ is a grid point.

Input

The only line contains two integers $n, m$ ( $1\le n, m\le 1000$ ).

Output

Print the answer in a single line.

Examples2

Example 1
Input
```
1 1
```
Expected output
```
0
```
Example 2
Input
```
2 3
```
Expected output
```
14
```