C. Bracket Subsequence
greedy
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.