Borderless Words

A word $w$ is called bordered if there exists a word $u$, other then $w$ and empty word $\varepsilon$, such that $u$ is both suffix and prefix if $w$. For example, a word <<abbababb>> is bordered because <<abb>> is both its prefix and its suffix. A word that is not bordered is called borderless. For example, a word <<aabab>> is borderless. 

Consider all borderless words of length $n$ composed of letters <<a>> and <<b>>. Let us denote the number of such words as $C\_n$. Order them lexicographically --- by the first letter, then by the second one, etc, and number from 1 to $C\_n$. Given $k$ find the $k$-th word in this order.

The input file contains multiple test cases.

Each test case contains two integers $n$ and $k$ on a line ($1 \le n \le 64$, $1 \le k \le C\_n$).

Input is followed by a line with $n = k = 0$. There are at most 1000 test cases in one input file.

For each test case output one line --- the $k$-th lexicographically borderless word of length $n$.