Knight move

The rectangular board of size $n\times m(n$ rows and $m$ columns) is given. The chess knight is located in the left upper corner. You must relocate it to the right lower corner. The knight can move only either two cells down and one right, or one cell down and two cells right.

Find the number of knight paths from the left upper corner to the right lower corner.

Input

Two positive integers $n$ and $m(1\le n,m\le 50)$.

Output

Print the number of ways to relocate the knight from the left upper corner to the right lower corner of the board.

Examples