Binary String

Problem Description

Komil loves working with perfect binary strings.

One day he wanted to create a binary string satisfying the following conditions:

• If you cut out any contiguous substring of length $N$, then the difference between the number of ones and the number of zeros in it equals $K$, i.e.: $(\text{number of } 1) - (\text{number of } 0) = K$
• If you cut out any contiguous substring of length $N + 2$, then the difference between the number of ones and the number of zeros in it is not equal to $K$, i.e.: $(\text{number of ones}) - (\text{number of zeros}) \neq K$

The longer Komil’s string is, the happier he is. If there are several strings of the same length, he chooses the lexicographically smallest one.

Your task is to find the perfect string using the given $N$ and $K$.

Input Format

The first line contains two integers $N$ and $K$.

Constraints:

• $2 \leq N \leq 10^4$
• $0 \leq K < N$
• It is guaranteed that such a binary string exists for the given $N$ and $K$.

Output Format

Print the lexicographically smallest of the longest binary strings satisfying the conditions.

Scoring

2 0

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