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.HashMap;
import java.util.Scanner;
import java.util.Stack;

public class CF504C {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int k = s.nextInt();
        String str = s.next();

        // int[] arr = new int[str.length()];
        Stack<Integer> stack = new Stack<>();
        char[] strArr = str.toCharArray();
        HashMap<Integer, Integer> map = new HashMap<>();
        for (int i = 0; i < strArr.length; i++) {
            if (strArr[i] == '(') {
                stack.push(i);
            } else {
                map.put(i, stack.pop());
            }
        }
        int i = n;
        int j = 0;
        while (i != k) {
            if (strArr[j] == ')') {
                strArr[j] = '$';
                strArr[map.get(j)] = '$';
                i -= 2;
            }
            j++;
        }

        StringBuilder ans = new StringBuilder();
        for (int l = 0; l < strArr.length; l++) {
            if (strArr[l] != '$') {
                ans.append(strArr[l]);
            }
        }
        System.out.println(ans.toString());

    }
}
