C. Bracket Subsequencetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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.InputThe 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.OutputPrint 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.ExamplesInput6 4()(())Output()()Input8 8(()(()))Output(()(()))
Input6 4()(())
Output()()
['greedy', '*1200']