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.BufferedInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.PrintWriter;
import java.util.ArrayList;

public class C {

	static int next[], prev[];
	static boolean gone[];
	static int N;
	public static void main(String[] args) {
		JS in = new JS();
		PrintWriter out = new PrintWriter(System.out);
		N = in.nextInt();
		int K = in.nextInt();
		char c[] = in.next().toCharArray();
		ArrayList<Integer> find = new ArrayList<Integer>();
		for(int i = 0; i < N-1; i++) {
			if(c[i] == '(' && c[i+1] == ')') find.add(i);
		}
		next = new int[N];
		prev = new int[N];
		for(int i = 0; i < N; i++) {
			next[i] = i+1;
			prev[i] = i-1;
		}
		
		
		int cur = N;
		gone = new boolean[N];
		for(Integer id : find) {
			if(cur == K) break;
			int l = id;
			int r = id+1;
			while(true) {
				//System.out.println(l+" "+r+"  "+c[l]+" "+c[r]);
				gone[l]=true;
				gone[r]=true;
				cur-=2;
				if(cur==K)break;
				l = prev(l);
				r = next(r);
				//System.out.println("  ->"+l+" "+r);
				if(l < 0 || r >= N) break;
				if(c[l] == ')' || c[r] == '(') break;
			}
		}
		for(int i = 0; i < N; i++) {
			if(!gone[i])out.print(c[i]);
		}out.println();
		out.close();
		
	}
	
	static int next(int i) {
		if(i == N-1 || next[i] >= N) return next[i] = N;
		if(!gone[next[i]]) return next[i];
		else return next[i] = next(i+1);
	}
	static int prev(int i) {
		if(i == 0 || prev[i] < 0) return prev[i] = -1;
		if(!gone[prev[i]]) return prev[i];
		else return prev[i] = prev(i-1);
	}

	
	static class JS{
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;
		
		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}
		
		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}
		
		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}				
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}
		
		public int nextInt() {
			return (int)nextLong();
		}
		
		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}
		
		public double nextDouble() {
		    while(c!='.'&&c!='-'&&(c <'0' || c>'9')) c = nextChar();
		    boolean neg = c=='-';
		    if(neg)c=nextChar();
		    boolean fl = c=='.';
		    double cur = nextLong();
		    if(fl) return neg ? -cur/num : cur/num;
		    if(c == '.') {
			double next = nextLong();
			return neg ? -cur-next/num : cur+next/num;
		    }
		    else return neg ? -cur : cur;
		}
		
		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}
		
		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}
	
}
