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 ≤ n ≤ 50 and 1 ≤ x ≤ 26.
Output
Print, in alphabetic order, all the antipalindromic words of length n that can be made up with the first x lowercase letters.
Input
8 3
Output
abcabcab acbacbac bacbacba bcabcabc cabcabca cbacbacb
Input
3 4
Output
abc abd acb acd adb adc bac bad bca bcd bda bdc cab cad cba cbd cda cdb dab dac dba dbc dca dcb