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≤k≤n≤2⋅105, 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
(()(()))
(()(()))
