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.io.*;
import java.util.*;

import static java.lang.Double.parseDouble;
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.util.Arrays.stream;
import static java.util.stream.IntStream.range;

/**
 * Created by prituladima on 5/23/18.
 */
public final class C {

    private void solve() {


        int n = nextInt(), k = nextInt();
        String s = nextToken();
        char[] chars = s.toCharArray();


        int diff = (n - k) / 2;
//        int b = diff;
        LinkedList<Character> stack = new LinkedList<>();
        for (int i = 0; i < chars.length; i++) {
            if (diff == 0)
                stack.addLast(chars[i]);
            else {
                if (chars[i] == '(')
                    stack.addLast(chars[i]);
                else {
                    stack.removeLast();
                    diff--;
                }
            }
        }

        for (char cur : stack) {
            sout(cur);
        }

    }

    public static void main(String[] args) {
        new C().run();
    }

    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter writer;

    private void run() {
        try {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = null;
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    private int nextInt() {
        return parseInt(nextToken());
    }

    private long nextLong() {
        return parseLong(nextToken());
    }

    private double nextDouble() {
        return parseDouble(nextToken());
    }

    private int[] nextArr(int size) {
        return stream(new int[size]).map(c -> nextInt()).toArray();
    }

    private long[] nextArrL(int size) {
        return stream(new long[size]).map(c -> nextLong()).toArray();
    }

    private double[] nextArrD(int size) {
        return stream(new double[size]).map(c -> nextDouble()).toArray();
    }

    private char[][] nextCharMatrix(int n) {
        return range(0, n).mapToObj(i -> nextToken().toCharArray()).toArray(char[][]::new);
    }

    private int[][] nextIntMatrix(final int n, final int m) {
        return range(0, n).mapToObj(i -> nextArr(m)).toArray(int[][]::new);
    }

    private double[][] nextDoubleMatrix(int n, int m) {
        return range(0, n).mapToObj(i -> nextArr(m)).toArray(double[][]::new);
    }

    private String nextToken() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    private void souf(String format, Object... args) {
        writer.printf(format, args);
    }

    private void sout(Object o) {
        writer.print(o);
    }

    private void newLine() {
        writer.println();
    }

    private void soutnl(Object o) {
        sout(o);
        newLine();
    }

    private int max(int a, int b) {
        return Math.max(a, b);
    }

    private int min(int a, int b) {
        return Math.min(a, b);
    }

}