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

(()(()))
"""Problem C - Bracket Subsequence.

https://codeforces.com/contest/1023/problem/C

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.

"""
import logging


fmt = r'%(levelname)s - %(name)s (line:%(lineno)s) - %(message)s'
formatter = logging.Formatter(fmt)

ch = logging.StreamHandler()
ch.setLevel(logging.ERROR)
ch.setFormatter(formatter)

logger = logging.getLogger('bracket_subsequence')
logger.setLevel(logging.ERROR)
logger.addHandler(ch)


# class Bracket:
#     def __init__(self):
#         self.children = []
    
#     def add(self, s):
#         pass
    
#     def remove(self, child=0):
#         if self.children[child].has_children():
#             self.children[child].remove()


def parse(s):
    stack = []
    for i, c in enumerate(s):
        if c == ')':
            idx = stack.pop()
            yield (idx, i)
        else:
            stack.append(i)


def solve(k, s):
    # if len(s) == 2 * k:
    #     return s

    indices = parse(s)
    sorted_indices = sorted(indices, key=lambda x: x[1] - x[0], reverse=True)
    # print(sorted_indices)
    res = sorted_indices[:k // 2]
    # print('>', res)

    ans = [0] * len(s)
    for i, j in res:
        ans[i] = '('
        ans[j] = ')'
    # print(ans)
    sol = [x for x in ans if x != 0]
    # print(sol)
    return ''.join(sol)


def main():
    n, k = map(int, input().strip().split())
    s = input().strip()

    result = solve(k, s)
    print(result)


if __name__ == '__main__':
    main()
