In this problem we consider the expressions defined as follows:
For instance, if the set of variables is A, B, C, these are some correct expressions:
A (A) ((C)) (A)−(B) ((A)−(B))−(A) |
Write a program that, given two numbers n and m, prints the number of correct expressions of length exactly n that can be made up with m variables.
For instance, for n =7 and m=2 the result should be 6, corresponding to
(((A))) (((B))) (A)−(A) (A)−(B) (B)−(A) (B)−(B) |
Input
Input consists of several cases, each with two natural numbers n and m between 1 and 25.
Output
For every case, print the number of correct expressions of length exactly n that can be made up with m variables. This number will always be smaller than 10^{9}.
Input
7 2 1 20 20 1 21 1 25 25
Output
6 20 0 212 307378150