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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
        public static void main(String[] args) {
                new Thread(null, new Runnable() {
                        public void run() {
                                new Main().solve();
                        }
                }, "1", 1 << 26).start();
        }

        void solve() {
                InputStream inputStream = System.in;
                OutputStream outputStream = System.out;
                ScanReader in = new ScanReader(inputStream);
                PrintWriter out = new PrintWriter(outputStream);
                CBracketSubsequence solver = new CBracketSubsequence();
                solver.solve(1, in, out);
                out.close();
        }

        static class CBracketSubsequence {
                public void solve(int testNumber, ScanReader in, PrintWriter out) {
                        int n = in.scanInt();
                        int k = in.scanInt();
                        int tt = 0;
                        char[] ar = in.scanString().toCharArray();
                        int[] ans = new int[k];
                        int sum = 0;
                        int[] tl = new int[n + 1];
                        for (int i = n - 1; i >= 0; i--) {
                                tl[i] += tl[i + 1];
                                if (ar[i] == ')') tl[i]++;
                        }
                        for (int i = 0; i < n && tt < k; i++) {
                                if (ar[i] == '(') {
                                        if (sum + 1 <= tl[i + 1] && k - (tt + 1) >= sum + 1) {
                                                ans[tt] = 0;
                                                sum++;
                                                tt++;
                                        }
                                } else {
                                        if (sum > 0) {
                                                ans[tt] = 1;
                                                sum--;
                                                tt++;
                                        }
                                }
                        }
                        if (tt != k || sum != 0) throw new RuntimeException("NO");
                        for (int i = 0; i < k; i++) {
                                if (ans[i] == 0) out.print("(");
                                else out.print(")");
                        }
                }

        }

        static class ScanReader {
                private byte[] buf = new byte[4 * 1024];
                private int index;
                private BufferedInputStream in;
                private int total;

                public ScanReader(InputStream inputStream) {
                        in = new BufferedInputStream(inputStream);
                }

                private int scan() {
                        if (index >= total) {
                                index = 0;
                                try {
                                        total = in.read(buf);
                                } catch (Exception e) {
                                        e.printStackTrace();
                                }
                                if (total <= 0) return -1;
                        }
                        return buf[index++];
                }

                public int scanInt() {
                        int integer = 0;
                        int n = scan();
                        while (isWhiteSpace(n)) n = scan();
                        int neg = 1;
                        if (n == '-') {
                                neg = -1;
                                n = scan();
                        }
                        while (!isWhiteSpace(n)) {
                                if (n >= '0' && n <= '9') {
                                        integer *= 10;
                                        integer += n - '0';
                                        n = scan();
                                }
                        }
                        return neg * integer;
                }

                public String scanString() {
                        int c = scan();
                        if (c == -1) return null;
                        while (isWhiteSpace(c)) c = scan();
                        StringBuilder res = new StringBuilder();
                        do {
                                res.appendCodePoint(c);
                                c = scan();
                        } while (!isWhiteSpace(c));
                        return res.toString();
                }

                private boolean isWhiteSpace(int n) {
                        if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
                        else return false;
                }

        }
}

