B. Count the Number of Pairstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputKristina has a string s of length n, consisting only of lowercase and uppercase Latin letters. For each pair of lowercase letter and its matching uppercase letter, Kristina can get 1 burl. However, pairs of characters cannot overlap, so each character can only be in one pair.For example, if she has the string s = "aAaaBACacbE", she can get a burl for the following character pairs:   s_1 = "a" and s_2 = "A"  s_4 = "a" and s_6 = "A"  s_5 = "B" and s_{10} = "b"  s_7= "C" and s_9 = "c" Kristina wants to get more burles for her string, so she is going to perform no more than k operations on it. In one operation, she can:  either select the lowercase character s_i (1 \le i \le n) and make it uppercase.  or select uppercase character s_i (1 \le i \le n) and make it lowercase. For example, when k = 2 and s = "aAaaBACacbE" it can perform one operation: choose s_3 = "a" and make it uppercase. Then she will get another pair of s_3 = "A" and s_8 = "a"Find maximum number of burles Kristina can get for her string.InputThe first line of input data contains a single integer t (1 \le t \le 10^4) — the number of test cases.The description of the test cases follows.The first line of each test case contains two integers n (1 \le n \le 2 \cdot 10^5) and k (0 \le k \le n) — the number of characters in the string and the maximum number of operations that can be performed on it.The second line of each test case contains a string s of length n, consisting only of lowercase and uppercase Latin letters.It is guaranteed that the sum of n over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, print exactly one integer on a separate line: the maximum number of burles that Kristina can get for her string s.ExampleInput
511 2aAaaBACacbE2 2ab4 1aaBB6 0abBAcC5 3cbccbOutput
5
0
1
3
2
NoteThe first test case is explained in the problem statement.In the second test case, it is not possible to get any pair by performing any number of operations.
511 2aAaaBACacbE2 2ab4 1aaBB6 0abBAcC5 3cbccb
5 0 1 3 2 
['greedy', 'strings', '*1000']