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.

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 $ .

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.

6 4
()(())

()()

8 8
(()(()))

(()(()))