Description

In daily routines, people prefer to sort binary strings of length $n$ lexicographically. For example, if we sort binary strings of length $2$ increasingly, we will get: $00$, $01$, $10$, $11$.

Gray Code is a special sorting method to sort binary strings of length $n$. It requires adjacent binary strings to have exactly one bit different. Specifically, the first string and the last string are also considered adjacent.

One example of binary strings of length $2$s sorted in Gray Code is: $00$, $01$, $11$, $10$.

There can be multiple Gray Codes of length $n$. The following is an algorithm for generating one of the Gray Codes:

1. Gray Code of length $1$ contains two binary strings of length $1$, with the order: $0$, $1$.
2. The first $2^n$ binary strings in Gray Code of length $n+1$ can be generated by adding a prefix $0$ to Gray Code of length $n$ ($2^n$ binary strings of length $n$ in total) sorted in order.
3. The last $2^n$ binary strings in Gray Code of length $n+1$ can be generated by adding a prefix $1$ to Gray Code of length $n$ ($2^n$ binary strings of length $n$ in total) sorted in reverse order.

In short, Gray Code of length $n+1$ is formed by adding a prefix $0$ to sorted Gray Code of length $n$, and adding a prefix $1$ to reversely sorted Gray Code of length $n$, to obtain $2^{n+1}$ binary strings in total. Additionally, for the $2^n$ binary strings in Gray Code of length $n$, we will label them from $0$ to $2^n-1$ in order.

Using this algorithm, Gray Code of length $2$ can be generated as follow:

1. It's known that Gray Code of length $1$ is $0$, $1$.
2. The first $2$ strings in Gray Code of length $2$ are: $00$, $01$. The last $2$ are: $11$, $10$. Combining them, we get $00$, $01$, $11$, $10$. The labels are $0,1,2,3$.

Gray Code of length $3$ follows the same rule:

1. It's known that Gray Code of length $2$ is $00$, $01$, $11$, $10$.
2. The first $4$ strings in Gray Code of length $3$ are: $000$, $001$, $011$, $010$. The last $4$ are: $110$, $111$, $101$, $100$. Combining them, we get $000$, $001$, $011$, $010$, $110$, $111$, $101$, $100$. The labels are $0,1,2,\dots,7$.

You are given $n$ and $k$. Find the $k$-th binary string (the string with label $k$) in Gray Code of length $n$, generated by the algorithm above.

Input Format

The only line of the input contains two integers: $n$ and $k$.

Output Format

Print a single binary string of length $n$ denoting the answer.

2 3

10

3 5

111

Constraints

For $50\%$ of the data, $n\le 10$;
For $80\%$ of the data, $k \le 5\times 10^6$;
For $95\%$ of the data, $k\le 2^{63}-1$;
For $100\%$ of the data, $1\le n \le 64$, $0\le k < 2^n$.