#P1158B. The minimal unique substring
The minimal unique substring
Description
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.
Input
The first line contains two integers $n$ and $k$, separated by spaces ($1 \leq k \leq n \leq 100\,000$, $(k \bmod 2) = (n \bmod 2)$).
Output
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.
Samples
4 4
1111
5 3
01010
7 3
1011011
Note
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 $3$.