CF1158B.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.

In the first test, it's easy to see, that the only unique substring of string $s = $ "1111" is all string $s$ , which has length $4$ .

In the second test a string $s = $ "01010" has minimal unique substring $t =$ "101", which has length $3$ .

In the third test a string $s = $ "1011011" has minimal unique substring $t =$ "110", which has length $3$ .