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 d2prac implements Runnable 
{
	private boolean console=false;
	 
	public void solve()
	{
		int i; int n=in.ni(); int k=in.ni();
		char a[]=in.ns().toCharArray(); int f=0; int done=0; Stack<Integer> op=new Stack(); 
		String ans="";
		int val[]=new int[n];
		for(i=0;i<n;i++)
		{
			if(a[i]=='(')
				op.add(i);
			else
			{
				if(op.size()>0)
				{
					val[op.pop()]=1; val[i]=2; done++; 
				}
			}
			if(done==k/2)
				break;
		}
		for(i=0;i<n;i++)
		{
			if(val[i]==1)
				out.print("(");
			else if(val[i]==2)
				out.print(")");
		}
		out.println();
	}
	@Override
	public void run() {
		try {  init();  } 
		catch (FileNotFoundException e) {  e.printStackTrace();   }

		int t= 1;

		while (t-->0) {
			solve();
			out.flush(); }
	}
	private FastInput in;    private PrintWriter out;
	public static void main(String[] args) throws Exception {	 new d2prac().run();	 }

	private void init() throws FileNotFoundException {
		InputStream inputStream = System.in; 	 OutputStream outputStream = System.out;
		try {  if (!console && System.getProperty("user.name").equals("sachan")) {
			outputStream = new FileOutputStream("/home/sachan/Desktop/output.txt");
			inputStream = new FileInputStream("/home/sachan/Desktop/input.txt");   	}
		}	catch (Exception ignored) {	}
		out = new PrintWriter(outputStream); 	 in = new FastInput(inputStream);
	}
	static class FastInput { InputStream obj;
	public FastInput(InputStream obj) {	this.obj = obj;	}
	byte inbuffer[] = new byte[1024];  int lenbuffer = 0, ptrbuffer = 0;
	int readByte() { if (lenbuffer == -1) throw new InputMismatchException();
	if (ptrbuffer >= lenbuffer) { ptrbuffer = 0;
	try { lenbuffer = obj.read(inbuffer);  }
	catch (IOException e) { throw new InputMismatchException(); } }    
	if (lenbuffer <= 0) return -1;return inbuffer[ptrbuffer++]; }

	String ns() { int b = skip();StringBuilder sb = new StringBuilder();
	while (!(isSpaceChar(b)))	  { sb.appendCodePoint(b);b = readByte(); }return sb.toString();}

	int ni() { int num = 0, b;boolean minus = false;
	while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
	if (b == '-') { minus = true;b = readByte(); }
	while (true) { if (b >= '0' && b <= '9') { num = num * 10 + (b - '0'); } else {
		return minus ? -num : num; }b = readByte(); }}

	long nl() { long num = 0;int b;boolean minus = false;
	while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
	if (b == '-') { minus = true;b = readByte(); }
	while (true) { if (b >= '0' && b <= '9') { num = num * 10L + (b - '0'); } else {
		return minus ? -num : num; }b = readByte(); } }

	boolean isSpaceChar(int c) { return (!(c >= 33 && c <= 126)); }
	int skip() { int b;while ((b = readByte()) != -1 && isSpaceChar(b)) ;return b; }
	float nf() {return Float.parseFloat(ns());}
	double nd() {return Double.parseDouble(ns());}
	char nc() {return (char) skip();}
	}
}


