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:

Input: s = "(())", k = 1

Output: ""

Explanation:

k-balanced substring is "()"

Step Current s k-balanced Result s
1 (()) (()) ()
2 () () Empty

Thus, the final string is "".

Example 2:

Input: s = "(()(", k = 1

Output: "(("

Explanation:

k-balanced substring is "()"

Step Current s k-balanced Result s
1 (()( (()( ((
2 (( - ((

Thus, the final string is "((".

Example 3:

Input: s = "((()))()()()", k = 3

Output: "()()()"

Explanation:

k-balanced substring is "((()))"

Step Current s k-balanced Result s
1 ((()))()()() ((()))()()() ()()()
2 ()()() - ()()()

Thus, the final string is "()()()".

 

Constraints: