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 Bracket_Subsequence
{
    public static void main(String args[])
    {
        Scanner s1 = new Scanner(System.in);
        int n,k;
        n = s1.nextInt();
        k = s1.nextInt();
        String seq = s1.next();
        if(n == k)
            System.out.println(seq);
        else
        {
            int diff = n - k;
            int s = 0, e = 0;
            StringBuilder sb = new StringBuilder();
            for(int i=0;i<n;i++)
            {
                if(seq.charAt(i) == '(')
                {
                    s++;
                    if(s > diff / 2)
                        sb.append(seq.charAt(i));
                }
                else if(seq.charAt(i) == ')')
                {
                    e++;
                    if(e > diff / 2)
                        sb.append(seq.charAt(i));
                }
            }
            System.out.println(sb.toString());
        }
        s1.close();
    }
}