|Kotlin Heroes: Episode 6|
A bracket sequence is a string containing only characters "(" and ")". A regular bracket sequence (or, shortly, an RBS) 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:
You are given a string $$$s$$$, which is an RBS. You can apply any number of operations to this string. Each operation can have one of the following types:
The operation $$$2$$$ can be applied at most $$$k$$$ times. Calculate the maximum number of operations you can apply until $$$s$$$ becomes empty.
The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^5$$$) — the number of test cases.
Each test case is described by two lines. The first line contains two integers $$$n$$$ and $$$k$$$ ($$$2 \le n \le 2 \cdot 10^5$$$; $$$1 \le k \le n$$$; $$$n$$$ is even) — the length of $$$s$$$ and the maximum number of operations of type $$$2$$$ you can apply.
The second line contains a string $$$s$$$ of $$$n$$$ characters '(' and ')'. This string is an RBS.
The sum of $$$n$$$ over all test cases doesn't exceed $$$2 \cdot 10^5$$$.
For each test case, print one integer — the maximum number of operations you can apply.
3 12 2 (()())((())) 6 3 ()()() 8 1 (((())))
4 3 2