Ouroboros Snake

Ouroboros is a mythical snake from ancient Egypt. It holds its tail in its mouth and continuously devours itself.

The Ouroboros numbers are binary numbers of $2^n$ bits that have the property of "generating" every number from $0$ to $2^n-1$. The generation works as follows: given an Ouroboros number, place its $2^n$ bits around a circle. Then, moving the starting position one step at a time, read $2^n$ groups of $n$ consecutive bits along the circle. Such a circle is called the Ouroboros circle for size $n$. For each $n$ we work only with the smallest Ouroboros number.

For example, for $n = 2$ there are only four Ouroboros numbers: $0011$, $0110$, $1100$, and $1001$. The smallest one is $0011$. The figure below shows the Ouroboros circle for $0011$.

The function $o(n; k)$ returns the value of the group that starts at position $k$ in the Ouroboros circle of the smallest Ouroboros number of size $n$. Positions are numbered from $0$; starting at position $k$, read $n$ consecutive bits along the circle and interpret them as a binary number (the bit at the starting position $k$ is the most significant bit). Your program must compute this function $o(n; k)$.

The input consists of several test cases. Each test case is a line containing two integers $n$ and $k$ ($1 \le n \le 15$, $0 \le k < 2^n$). The end of the input is indicated by a line containing two zeros, which must not be processed.

For each test case, output the value of $o(n; k)$ on a line by itself.