Lyndon's Words#5439
In combinatorics, a Lyndon word of length over an alphabet is a string composed of symbols from this alphabet, which is strictly smaller than all of its proper suffixes. Lyndon words are also referred to as primitive strings.
For instance, using the alphabet \Sigma = \{a, b\} with the usual order (a < b), there are six distinct Lyndon words of length n = 5: "aaaab", "aaabb", "aabab", "aabbb", "ababb", and "abbbb".
Given and , your task is to find the -th lexicographical Lyndon word of length over the alphabet \Sigma = \{a, b\}. The words are indexed starting from one.
The first line of the input contains two integers and , separated by a space, representing the length and the ordinal number of the Lyndon word, respectively (1 \le n \le 25). It is guaranteed that a word of length with the specified number exists.
Output the required Lyndon word on the first line.
Example 1