Problem Statement

Snuke has written on a blackboard every integer from $1$ through $(2^N-1)$, in binary.

Find the $X$-th lexicographically smallest string when seeing the integers on the blackboard as strings.

Here, the input gives $N$ in decimal, but $X$ in binary.

Constraints

• $1 \leq N \leq 10^6$
• $1 \leq X \leq 2^N-1$
• $X$ is in binary.

Input

Input is given from Standard Input in the following format:

N
X

Output

Print the answer.