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

(()(()))
//package competitiveprogramming.2018.07_aug.cf_round_504;

import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Stack;

public class C {

    boolean ONLINE_JUDGE = (System.getProperty("ONLINE_JUDGE") != null);

    public C() throws IOException {
        InputReader in;
        if (ONLINE_JUDGE) {
            in = new InputReader(System.in);
        } else {
            in = new InputReader(new FileInputStream("/Users/karj/Competitive Programming/input.txt"));
        }
        PrintWriter out = new PrintWriter(System.out);

        int T = 1;
        for (int caseNo = 1; caseNo <= T; caseNo++) {
            solve(caseNo, in, out);
        }

        out.close();
    }

    private void solve(int caseNo, InputReader in, PrintWriter out) throws IOException {
        int N = in.nextInteger(), K = in.nextInteger();
        char S[] = new char[N];
        boolean removed[] = new boolean[N];
        S = in.nextString().toCharArray();
        if (N == K) {
            out.println(S);
            return;
        }
        int outLength = N;
        Stack<Integer> stack = new Stack<>();
        for (int i = 0; i < N; i++) {
            if (S[i] == '(') {
                stack.push(i);
            } else {
                int rem = stack.pop();
                removed[i] = true;
                removed[rem] = true;
                outLength -= 2;
                if (outLength == K) {
                    break;
                }
            }
        }
        for (int i = 0; i < N; i++) {
            if (!removed[i]) {
                out.print(S[i]);
            }
        }
        out.println();
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public interface SpaceCharFilter {

            public boolean isSpaceChar(int ch);
        }

        public String next() {
            return nextString();
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInteger() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public Long nextLong() {
            return Long.parseLong(nextString());
        }

        public Double nextDouble() {
            return Double.parseDouble(nextString());
        }
        
        public char nextCharacter() {
            return nextString().charAt(0);
        }
    }

    private void debug(Object... o) {
        if (ONLINE_JUDGE) {
            return;
        }
        System.out.println(Arrays.deepToString(o));
    }

    public static void main(String args[]) throws IOException {
        new C();
    }
}
