CF1023C.Bracket Subsequence

A bracket sequence is a string containing only characters "(" and ")". A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.

Subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

You are given a regular bracket sequence $s$ and an integer number $k$. Your task is to find a regular bracket sequence of length exactly $k$ such that it is also a subsequence of $s$.

It is guaranteed that such sequence always exists.

括号序列是指仅由字符 ( 和 ) 组成的字符串。正则括号序列（regular bracket sequence）是一种括号序列，它可以通过在原序列的字符之间插入字符 1 和 +，从而转化为一个合法的算术表达式。例如，括号序列 "()()" 和 "(())" 是正则的（对应的表达式分别为 "(1)+(1)" 和 "((1+1)+1)"），而 ")(", "(" 和 ")" 则不是。

子序列（subsequence）是指从另一个序列中删除若干元素（可以是零个）后，不改变剩余元素相对顺序所得到的序列。

给定一个正则括号序列 $s$ 和一个整数 $k$。你的任务是找出一个长度恰好为 $k$ 的正则括号序列，且该序列同时是 $s$ 的子序列。

题目保证这样的序列一定存在。

The first line contains two integers $n$ and $k$ ($2 \le k \le n \le 2 \cdot 10^5$, both $n$ and $k$ are even) — the length of $s$ and the length of the sequence you are asked to find.

The second line is a string $s$ — regular bracket sequence of length $n$.

第一行包含两个整数 $n$ 和 $k$（$2 \le k \le n \le 2 \cdot 10^5$，且 $n$ 和 $k$ 均为偶数）—— 分别表示字符串 $s$ 的长度以及所要求的子序列的长度。

第二行为一个字符串 $s$ —— 长度为 $n$ 的合法括号序列。

Print a single string — a regular bracket sequence of length exactly $k$ such that it is also a subsequence of $s$.

It is guaranteed that such sequence always exists.

输出一个字符串——该字符串是一个长度恰好为 $k$ 的合法括号序列，且它也是 $s$ 的一个子序列。

保证这样的序列一定存在。