Antipalindromic words P89248

In this problem, we say that a word is antipalindromic if it does not contain any subword that is a palindrome (with the exception of empty subwords and single letters). Write a program that prints all the antipalindromic words of length $n$ that can be made up with the first $x$ lowercase letters.

Input

Input consists of $n$ and $x$. Suppose $1 \le n \le 50$ and $1 \le x \le 26$.

Output

Print, in alphabetic order, all the antipalindromic words of length $n$ that can be made up with the first $x$ lowercase letters.