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.

Input

Input is given from Standard Input in the following format:
N
X

Output

Print the answer.

Constraints

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

Sample Input 1

3
101

Sample Output 1

11

The strings written on the blackboard in lexicographical order are 1, 10, 100, 101, 11, 110, 111.
Additionally, we have $X=101(\mathrm{binary})=5(\mathrm{decimal})$.
Thus, the answer is 11.

Sample Input 2

10
10100011

Sample Output 2

1001001111

Sample Input 3

1000000
11111

Sample Output 3

1000000000000000000000000000000

见题面 Input 部分

见题面 Output 部分