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

(()(()))

from collections import deque
import sys
input = sys.stdin.readline
print = sys.stdout.write
def main():
	
	n,k = map(int,input().split())
	s = input()
	n2 = list(s)
	si = deque()
	inc = 0
	for x in range(n):
		if s[x] == "(":
			si.append(x)
		if s[x] == ")":
			n2[si.popleft()] = "."
			n2[x] = "."
			inc += 1
			if inc == k//2:
				break
	s2 = ""
	for x in range(n):
		if n2[x] == ".":
			print(s[x])
	print("\n")

main()