Correct expressions

In this problem we consider the expressions defined as follows:

Every variable is a correct expresion;
if $x$ is a correct expression, so is $(x)$ ;
if $x_1$ and $x_2$ are correct expressions, so are $(x_1) - (x_2)$ ;
nothing else is a correct expression.

For instance, if the set of variables is ${A, B, C}$ , these are some correct expressions:

$A \qquad (A) \qquad ((C)) \qquad (A)-(B) \qquad ((A)-(B))-(A)$

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

$(((A))) \qquad (((B))) \qquad (A)-(A) \qquad (A)-(B) \qquad (B)-(A) \qquad (B)-(B)$

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 $10^9$ .

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T11:37:05.828Z