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 Program
{
	public static void main(String[] args) {
		   Scanner sc = new Scanner(System.in);
		   int n = sc.nextInt();
		   int k = sc.nextInt();
		   int i = 0;
		   String s = sc.next();
		   
		   
    	    int o = k/2;
            int c = k/2;
    	   for(char str : s.toCharArray()){
    	        if(str =='(' && o!= 0){
    	            o--;
    	            System.out.print(str);
    	        } else if(c != 0 && str == ')'){
    	            c--;
    	            System.out.print(str);
    	        }
    	   }
	}
}