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.Scanner;

public class PlainJavaApplication {

  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    String[] nAndK = scanner.nextLine().split(" ");
    int n = Integer.valueOf(nAndK[0]);
    int k = Integer.valueOf(nAndK[1]);
    String s = scanner.nextLine();

    System.out.println(getSubSequence(n, k, s));
  }

  public static String getSubSequence(int n, int k, String s) {
    int open = 0;
    int appended = 0;
    StringBuilder builder = new StringBuilder();
    for (int i = 0; i < s.length() && appended < k; i++) {
      char ch = s.charAt(i);
      if (ch == '(' && open >= k - appended) {
        continue;
      }
      if (ch == '(') {
        open++;
      } else {
        open--;
      }

      builder.append(ch);
      appended++;
    }

    return builder.toString();
  }

}
