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.*;
import java.math.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

     //--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<-------------------

public class a{ 
     static int[] count,count1,count2;
     static Node[] nodes;
     static int[] arr;
     static int[] dp;
     static char[] ch,ch1;
     static int[] darr,farr;
     static Character[][] mat,mat1;
     static long x,h;
     static long maxl;
     static double dec;
     static String s;
     static long minl;
     static int mx = (int)1e9+5;
     static long mod = 998244353l;
     // static int minl = -1;
     // static long n;
     static int n,n1,n2;
     static long a;
     static long b;
     static long c;
     static long d;
     static long y,z;
     static int m;
     static long k;
     static String[] str,str1;
     static Set<Long> set,set1,set2;
     static List<Integer> list1,list2,list3;
     static LinkedList<Character> ll;
     static Map<String,String> map;
     static StringBuilder sb,sb1,sb2;
     static int[] dx = {0,-1,0,1};
     static int[] dy = {-1,0,1,0};

     // public static void solve(){

     //    FastScanner sc = new FastScanner();

     //    long n = sc.nextLong();
     //    long m = sc.nextLong();

     //    for(int i = 0 ; i < m ; i++){

     //        long x = sc.nextLong();
     //        long y = sc.nextLong();

     //        long ans = 0;
     //        if(n%2 == 0){
     //            ans = (y+1)/2 + (n/2) * (x-1);
     //        }
     //        else{

     //            if(x%2 == 1){
     //                ans = (x-1)/2 * n + (y+1)/2;
     //            }
     //            else{
     //                ans = (x-2)/2 * n + (n+1)/2 + (y+1)/2 - (y%2);
     //            }
     //        }

     //        if((x+y)%2 != 0)
     //            ans += ((n*n + 1)/2);

     //        System.out.println(ans);

     //    }

        
     // }

     //--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<-------------------

     public static void solve(){

        int k = m/2;
        int l = 0;
        int r = n-1;
        int count = 0;
        ch1 = new char[n];

        for(int i = 0 ; i < n ; i++){
            if(ch[i] == '('){
                ch1[i] = '(';
                count += 1;
            }
            if(count == k)
                break;
        }

        count = k;
        for(int i = n-1 ; i > -1 ; i--){
            if(ch[i] == ')'){
                ch1[i] = ')';
                count -= 1;
            }
            if(count == 0)
                break;
        }

        sb = new StringBuilder();

        for(int i = 0 ; i < n ;i++)
            if(ch1[i] == ')' || ch1[i] == '(')
                sb.append(ch1[i]);  

        System.out.println(sb);
            
     }

     public static void main(String[] args) {

            FastScanner sc = new FastScanner();
            // Scanner sc = new Scanner(System.in);
            // int t = sc.nextInt();
            int t = 1;
            // int l = 1;
            while(t > 0){
                
                // n = sc.nextInt();
                // n = sc.nextLong();
                // a = sc.nextLong();
                // b = sc.nextLong();
                // c = sc.nextLong();
                // d = sc.nextLong();

                // x = sc.nextLong();
                // y = sc.nextLong();
                
                // n = sc.nextLong();
                n = sc.nextInt();
                // n1 = sc.nextInt();

                m = sc.nextInt();

                // k = sc.nextLong();
                // s = sc.next();

                ch = sc.next().toCharArray();
                // ch1 = sc.next().toCharArray();

                // arr = new int[n];
                // for(int i = 0 ; i < n ; i++){
                //     arr[i] = sc.nextInt();
                // }
                // m = n;
                // darr = new int[m];
                // for(int i = 0; i < m ; i++){
                //     darr[i] = sc.nextInt();
                // }

                // farr = new int[n];
                // for(int i = 0; i < n ; i++){
                //     farr[i] = sc.nextInt();
                // }

                // mat = new Character[n][m];
                // for(int i = 0 ; i < n ; i++){
                //     String s = sc.next();
                //     for(int j = 0 ; j < m ; j++){
                //         mat[i][j] = s.charAt(j);
                //     }
                // }
                // str = new String[n];
                // for(int i = 0 ; i < n ; i++)
                //     str[i] = sc.next();

                // nodes = new Node[n];
                // for(int i = 0 ; i < n ;i++)
                //     nodes[i] = new Node(sc.nextInt(),sc.nextInt());

                // System.out.println(solve()?"YES":"NO");
                 solve();       
                 // System.out.println(solve());
                 t -= 1;
            }

     }

    public static int log(long n){

         if(n == 0 || n == 1)
             return 0;

         if(n == 2)
             return 1;

         double num = Math.log(n);
         double den = Math.log(2);

         if(den == 0)
             return 0;

         return (int)(num/den);
     }

    public static boolean isPrime(long n) { 
    // Corner cases 
        if (n <= 1)  
            return false; 

        if (n <= 3)  
            return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n%2 == 0 || n%3 == 0) 
            return false; 
      
        for (int i=5; i*i<=n; i=i+6) 
            if (n%i == 0 || n%(i+2) == 0) 
               return false; 
      
        return true; 
    } 

     public static long gcd(long a,long b){

        if(b%a == 0){
            return a;
        }
        return gcd(b%a,a);

     }

     // public static void swap(int i,int j){
     //     long temp = arr[j];
     //     arr[j] = arr[i];
     //     arr[i] = temp;
     // } 

    static final Random random=new Random();
    
    static void ruffleSort(long[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static class Node{
        Integer first;
        Integer second;
        Node(Integer f,Integer s){
            this.first = f;
            this.second = s;
        }
    }

     static class FastScanner {

                BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                StringTokenizer st=new StringTokenizer("");
                String next() {
                        while (!st.hasMoreTokens())
                                try {
                                        st=new StringTokenizer(br.readLine());
                                } catch (IOException e) {
                                        e.printStackTrace();
                                }
                        return st.nextToken();
                }
                
                int nextInt() {
                        return Integer.parseInt(next());
                }
                int[] readArray(int n) {
                        int[] a=new int[n];
                        for (int i=0; i<n; i++) a[i]=nextInt();
                        return a;
                }
                long nextLong() {
                        return Long.parseLong(next());
                }
        }

}