Words with x, y and z X20680

In this problem we will consider words of size $n$, made from letters ‘x’, ‘y’ and ‘z’, and without more than $c$ equal consecutive letters. Write a program that writes all words that satisfy these constraints.

Input

Input consists of several cases, each with an $n$ between 1 and 15 and a $c$ between 1 and $n$.

Output

For each case, write in alphabetical order all words of length $n$ made from letters ‘x’, ‘y’ and ‘z’ that do not contain $c+1$ equal consecutive letters. Write a line with 20 hyphens at the end of each case.