Mondriaan's Dream#631
Squares and rectangles fascinated the famous Dutch painter Piet Mondriaan. One night, after producing the drawings in his "toilet series" (when he had to use his toilet paper to draw on, as all his other paper was filled with squares and rectangles), he dreamt of filling a large rectangle with small rectangles of width and height in different ways.
Expert as he was in this material, he immediately understood that he would need a computer to calculate the number of ways to fill a large rectangle whose dimensions are integer values. Help him, so that his dream does not turn into a nightmare!
The input file contains several test cases. Each test consists of two integers: the height and the width of the large rectangle. The input is terminated by the line h = w = 0. Otherwise, 1 \leq h, w \leq 11.
For each test case, output the number of different ways the given rectangle can be filled with small rectangles of size 2 \times 1. Assume the given large rectangle is oriented, i.e., count symmetrical tilings multiple times.
Example 1