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 MyClass {
    public static void main(String args[]) 
    {
       Scanner sc=new Scanner(System.in);
       int n=sc.nextInt();
       int k=sc.nextInt();
       String s=sc.next();
       int l=s.length();
       int ob=0;
       int cb=0;
       k=k/2;
       
       
       for(int i=0;i<l;i++)
       {
           if((s.charAt(i)=='(')&&(ob<k))
           {
               
               ob++;
               System.out.print("(");
           }
           else if((s.charAt(i)==')')&&(cb<ob))
           {
               
               cb++;
               System.out.print(")");
           }
       }
       
       
    }
}
