A. Tiling Dominoes 

Problem

Given a rectangular grid, with dimensions m x n, compute the number of ways of completely tiling it with dominoes. Note that if the rotation of one tiling matches another, they still count as different ones. A domino is a shape formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a matching in the grid graph formed by placing a vertex at the center of each square of the region and connecting two vertices when they correspond to adjacent squares. An example of a tiling is shown below.

The Input

The input will consist of a set of lines with m n, given the restriction n*m<101.

The Output

For each line of input, output the number of tilings in a separate line.

Sample Input

2 10
4 10
8 8

Sample Output

89
18061
12988816

Problem setter: Josh Bao
Alternative Solution: Rodrigo Burgos