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 $k$.

设 $s$ 是一个仅由字符 "0" 或 "1" 组成的字符串。若存在某个整数 $1 \leq l \leq |s| - |t| + 1$，使得 $t = s_l s_{l+1} \ldots s_{l + |t| - 1}$，则称字符串 $t$ 是字符串 $s$ 的一个子串。若满足上述条件的 $l$ 唯一，则称子串 $t$ 是字符串 $s$ 的一个唯一子串。

例如，设 $s = $"1010111"。字符串 $t = $"010" 是 $s$ 的一个唯一子串，因为只有 $l = 2$ 满足条件。但例如 $t = $"10" 就不是 $s$ 的唯一子串，因为 $l = 1$ 和 $l = 3$ 均满足条件。再如 $t =$"00" 根本不是 $s$ 的子串，因为不存在满足条件的 $l$。

今天，瓦夏（Vasya）在信息学课上解决了如下问题：给定一个仅由 "0" 和 "1" 组成的字符串，任务是找出其最短唯一子串的长度。他已为此问题编写了一个程序，现在希望测试它。他请你帮忙。

给定两个正整数 $n$ 和 $k$，满足 $(n \bmod 2) = (k \bmod 2)$（其中 $(x \bmod 2)$ 表示 $x$ 除以 $2$ 的余数）。请构造任意一个由 $n$ 个 "0" 或 "1" 组成的字符串 $s$，使得其最短唯一子串的长度恰好为 $k$。

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

第一行包含两个整数 $n$ 和 $k$，以空格分隔（$1 \leq k \leq n \leq 100\,000$，且 $(k \bmod 2) = (n \bmod 2)$）。

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.

打印一个长度为 $n$ 的字符串 $s$，该字符串仅由字符 "0" 和 "1" 组成，且 $s$ 的最短唯一子串的长度恰好为 $k$。你可以输出任意一个满足条件的字符串。题目保证至少存在一个满足条件的字符串。

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 $3$.

在第一个测试中，很容易看出字符串 $s = $"1111" 的唯一子串只有整个字符串 $s$，其长度为 $4$。

在第二个测试中，字符串 $s = $"01010" 的最短唯一子串为 $t =$"101"，其长度为 $3$。

在第三个测试中，字符串 $s = $"1011011" 的最短唯一子串为 $t =$"110"，其长度为 $3$。