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.InputStream;
import java.util.ArrayList;
import java.util.Stack;

public class SC
{
    static IO io = new IO(System.in);
    static int n, k;

    public static void main(String[] args) throws Exception
    {
        n = io.nextInt();   k = io.nextInt();
        String brack = io.next();
        boolean[] rem = new boolean[brack.length()];

        int i, j;
        Stack<Integer> ind1 = new Stack<>(), ind2 = new Stack<>();

        while(n > k)
        {
            if(ind1.isEmpty())
            {
                StringBuilder wtf = new StringBuilder();
                for(i = 0; i < brack.length(); ++i)
                    if(!rem[i])
                        wtf.append(brack.charAt(i));
                brack = wtf.toString();
                rem = new boolean[brack.length()];
                n = brack.length();
                ind1.clear();   ind2.clear();
                
                for(i = 0; i < brack.length() - 1; ++i)
                    if (brack.charAt(i) == '(' && brack.charAt(i+1) == ')') {
                        ind1.add(i);
                        ind2.add(i+1);
                    }
            }
            int i1 = ind1.pop(), i2 = ind2.pop();
            rem[i1--] = rem[i2++] = true;
            n -= 2;
            if(i1 < 0 || i2 >= brack.length() || brack.charAt(i1) != '(' || brack.charAt(i2) != ')');
            else
            {
                ind1.add(i1);   ind2.add(i2);
            }
        }
        //System.out.println(ind1);
        //System.out.println(ind2);
        for(i = 0; i < brack.length(); ++i)
            if(!rem[i])
                io.print(brack.charAt(i));
        io.flush();
    }
}

class IO
{
    static byte[] buf = new byte[2048];
    static int index, total;
    static InputStream in;
    static StringBuilder sb = new StringBuilder();


    IO(InputStream is)
    {
        in = is;
    }

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

    String next() throws Exception
    {
        int c;
        for(c=scan(); c<=32; c=scan());
        StringBuilder sb = new StringBuilder();
        for(; c>32; c=scan())
            sb.append((char)c);
        return sb.toString();
    }

    int nextInt() throws Exception
    {
        int c, val = 0;
        for(c=scan(); c<=32; c=scan());
        boolean neg = c=='-';
        if(c=='-' || c=='+')
            c = scan();
        for(; c>='0' && c<='9'; c=scan())
            val = (val<<3) + (val<<1) + (c&15);
        return neg?-val:val;
    }
    long nextLong() throws Exception
    {
        int c;long val = 0;
        for(c=scan(); c<=32; c=scan());
        boolean neg = c=='-';
        if(c=='-' || c=='+')
            c = scan();
        for(; c>='0' && c<='9'; c=scan())
            val = (val<<3) + (val<<1) + (c&15);
        return neg?-val:val;
    }
    void print(Object a)
    {
        sb.append(a.toString());
    }
    void println(Object a)
    {
        sb.append(a.toString()).append("\n");
    }
    void println()
    {
        sb.append("\n");
    }
    void flush()
    {
        System.out.print(sb);
        sb = new StringBuilder();
    }
}