You are given a string s consisting of '(' and ')', and an integer k.

A string is k-balanced if it is exactly k consecutive '(' followed by k consecutive ')', i.e., '(' * k + ')' * k.

For example, if k = 3, k-balanced is "((()))".

You must repeatedly remove all non-overlapping k-balanced substrings from s, and then join the remaining parts. Continue this process until no k-balanced substring exists.

Return the final string after all possible removals.

 

​​​​​​​Example 1:

Example 2:

Example 3:

 

Constraints:

• 2 <= s.length <= 105
• s consists only of '(' and ')'.
• 1 <= k <= s.length / 2