Statement

Hello, guys! Welcome to Jiangsu University of Technology.

Attracted by the campus structure, Timothy wishes to conduct research on it. He draws an $n\times m$ grid on the blackboard. The grid consists of $n+1$ vertical line segments and $m+1$ horizontal line segments. The vertical line segments intersect the horizontal line segments exactly at $(n+1)\times(m+1)$ points, forming $n\times m$ unit squares. We refer to these $(n+1)\times (m+1)$ intersection points as "grid points". Please output the number of line segments $\ell$ (not limited to vertical or horizontal line segments) that satisfy the following three conditions:

• The length is not zero.
• Both endpoints of $\ell$ are grid points.
• The midpoint of $\ell$ is also a grid point.

Input

One line contains two integers $n$ and $m$ separated by a space ($1\leqslant n, m\leqslant 1000$).

Output

Output an integer representing the number of line segments that satisfy the condition.

Samples

2 3

14

1 1

0