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.

Input

The first line contains two integers n and k (2 ≤ k ≤ n ≤ 2 ⋅ 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.

Output

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.

Examples

Input

6 4
()(())


Output

()()


Input

8 8
(()(()))


Output

(()(()))
import java.util.*;
public class round504_C
{
    public static void main(String args[])
    {
        Scanner sc=new Scanner (System.in);
        int n,k;
        String r[]=sc.nextLine().split(" ");
        n=Integer.parseInt(r[0]);
        k=Integer.parseInt(r[1]);
        String s=sc.nextLine();
        ArrayList<Integer> a=new ArrayList<Integer>();
        boolean v[]=new boolean[s.length()];
        int x=0;
        for(int i=0;i<s.length();i++)
        {
            if(s.charAt(i)=='(') a.add(i);
            else
            {
                if(a.isEmpty()) continue;
                else
                {
                       v[a.get(a.size()-1)]=true;
                       a.remove(a.size()-1);
                       v[i]=true;
                       x+=2;
                       if(x==k)break;
                }   
            }
        }
        for(int i=0;i<n;i++)
        {
            if(v[i]) System.out.print(s.charAt(i));
        }
        
    }
}