A12649 | The minimal unique substring

Let $s$ be some string consisting of symbols "0" or "1". Let's call a string $t$ a substring of string $s$ , if there exists such number $1 \leq l \leq |s| - |t| + 1$ that $t = s_l s_{l+1} \ldots s_{l + |t| - 1}$ . Let's call a substring $t$ of string $s$ unique, if there exist only one such $l$ .

For example, let $s = $ "1010111". A string $t = $ "010" is an unique substring of $s$ , because $l = 2$ is the only one suitable number. But, for example $t = $ "10" isn't a unique substring of $s$ , because $l = 1$ and $l = 3$ are suitable. And for example $t =$ "00" at all isn't a substring of $s$ , because there is no suitable $l$ .

Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him.

You are given $2$ positive integers $n$ and $k$ , such that $(n \bmod 2) = (k \bmod 2)$ , where $(x \bmod 2)$ is operation of taking remainder of $x$ by dividing on $2$ . Find any string $s$ consisting of $n$ symbols "0" or "1", such that the length of its minimal unique substring is equal to $k$ .

The first line contains two integers $n$ and $k$ , separated by spaces ( $1 \leq k \leq n \leq 100\,000$ , $(k \bmod 2) = (n \bmod 2)$ ).

Print a string $s$ of length $n$ , consisting of symbols "0" and "1". Minimal length of the unique substring of $s$ should be equal to $k$ . You can find any suitable string. It is guaranteed, that there exists at least one such string.