517. Cornerless Tiling

Time limit per test: 0.25 second(s)
Memory limit: 262144 kilobytes
input: standard
output: standard



An cornerless tiling of an mx n rectangle is such tiling of this rectangle with 1x 2 and 2x 1 dominoes that no four dominoes share a corner.

For example, here are the two possible cornerless tilings of 4x 4 square:

How many cornerless tilings of mx n rectangle are there?

Input
First and only line of the input file contains two integers m and n, 1 ≤ n, m ≤ 1000.

Output
In the only line of the output file write the sought number of tilings.

Example(s)
sample input
 
sample output
 
4 4

2