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.*;

public class Main
{
	public static void main(String[] args) throws Exception
	{
		// int t = ni();
		int t = 1;
		while(t-->0) {
			int n = ni();
			int k = ni();
			String s = ns();
			int count = (n-k)/2;
			int count1 = count;
			for(int i=0;i<n;i++){
				if(s.charAt(i) == '('){
					if(count == 0){
						ans.append('(');
					}
					else
					count--;
				}
				else 
				{
					if(count1 == 0){
						ans.append(')');
					}
					else
					count1--;
				}
			}
			sopln(ans);
		}
	}
	static final long mod=1000000007l;
    static StringBuilder ans=new StringBuilder();
	static Reader in=new Reader();
	static final double eps=1e-9;
 
	//////////////////////////////////
	////input functions/////////////////
	static int ni(){return Integer.parseInt(in.next());}
	static long nl(){return Long.parseLong(in.next());}
	static String ns(){return in.next();}
	static double nd(){return Double.parseDouble(in.next());}
	static int[] nia(int n){int a[]=new int[n];for(int i=0; i<n; i++)a[i]=ni();return a;}
	static int[] pnia(int n){int a[]=new int[n+1];for(int i=1; i<=n; i++)a[i]=ni();return a;}
	static long[] nla(int n){long a[]=new long[n];for(int i=0; i<n; i++)a[i]=nl();return a;}
	static String[] nsa(int n){String a[]=new String[n];for(int i=0; i<n; i++)a[i]=ns();return a;}
	static double[] nda(int n){double a[]=new double[n];for(int i=0; i<n; i++)a[i]=nd();return a;}
 
	//////output functions////////////////
	static void pr(Object a){ans.append(a+"\n");}
	static void pr(){ans.append("\n");}
	static void p(Object a){ans.append(a);}
	static void pra(int[]a){for(int i:a)ans.append(i+" ");ans.append("\n");}
	static void pra(long[]a){for(long i:a)ans.append(i+" ");ans.append("\n");}
	static void pra(String[]a){for(String i:a)ans.append(i+" ");ans.append("\n");}
	static void pra(double[]a){for(double i:a)ans.append(i+" ");ans.append("\n");}
	static void sop(Object a){System.out.print(a);}
	static void sopln(Object a){System.out.println(a);}
	static void flush(){System.out.print(ans);ans=new StringBuilder();}
 
	static void exit(){System.out.print(ans);System.exit(0);}
	static int min(int... a){int min=a[0];for(int i:a)min=Math.min(min, i);return min;}
	static int max(int... a){int max=a[0];for(int i:a)max=Math.max(max, i);return max;}	
	static int gcd(int... a){int gcd=a[0];for(int i:a)gcd=gcd(gcd, i);return gcd;}	
	static long min(long... a){long min=a[0];for(long i:a)min=Math.min(min, i);return min;}
	static long max(long... a){long max=a[0];for(long i:a)max=Math.max(max, i);return max;}	
	static long gcd(long... a){long gcd=a[0];for(long i:a)gcd=gcd(gcd, i);return gcd;}	
	static String pr(String a, long b){String c="";while(b>0){if(b%2==1)c=c.concat(a);a=a.concat(a);b>>=1;}return c;}
	static long powm(long a, long b, long m){long an=1;long c=a;while(b>0){if(b%2==1)an=(an*c)%m;c=(c*c)%m;b>>=1;}return an;}
	static int gcd(int a, int b){if(b==0)return a;return gcd(b, a%b);}
	static long gcd(long a, long b){if(b==0)return a;return gcd(b, a%b);}
 
	static class Reader {
        BufferedReader reader;
        StringTokenizer tokenizer;
        public Reader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }
        String next() {while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {tokenizer = new StringTokenizer(reader.readLine());}
				catch (IOException e) {throw new RuntimeException(e);}}
            return tokenizer.nextToken();}
        int nextInt() {return Integer.parseInt(next());}
        long nextLong() {return Long.parseLong(next());}
        double nextDouble() {return Double.parseDouble(next());}
    }
 
}
