B. RBS Deletiontime limit per test3 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputA 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:  bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)");  bracket sequences ")(", "(" and ")" are not. 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:  choose some non-empty prefix of s and remove it from s, so s is still an RBS. For example, we can apply this operation as follows: "(())()(())()()" \to "()()" (the first 10 characters are removed);  choose some contiguous non-empty substring of s and remove it from s, so s is still an RBS. For example, we can apply this operation as follows: "(())()(())()()" \to "(())()()()" (the characters from the 7-th to the 10-th are removed). The operation 2 can be applied at most k times. Calculate the maximum number of operations you can apply until s becomes empty.InputThe 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.OutputFor each test case, print one integer — the maximum number of operations you can apply.ExampleInput
3
12 2
(()())((()))
6 3
()()()
8 1
(((())))
Output
4
3
2

3
12 2
(()())((()))
6 3
()()()
8 1
(((())))

4 3 2 
['*special problem', 'greedy', '*1800']