Solve the programming task below in a Python markdown code block.
JJ has a binary string S of length N. JJ can perform the following operation on S:
Select an i such that 1 ≤ i ≤ N, and flip S_{i} (i.e. change 0 to 1 and 1 to 0)

JJ wants to minimize the number of inversions in S by performing the above operation at most K times. Can you help JJ do so?

Recall that a pair of indices (i, j) in S is called an inversion if i < j and S_{i} > S_{j}.

------ Input Format ------ 

- The first line contains a single integer T - the number of test cases. Then the test cases follow.
- The first line of each test case contains two integers N and K - the length of the binary string S and the maximum number of times JJ can perform the given operation.
- The second line of each test case contains a binary string S of length N containing 0s and 1s only.

------ Output Format ------ 

For each test case, output the minimum number of inversions possible after performing the given operation at most K times.

------ Constraints ------ 

$1 ≤ T ≤ 10^{5}$
$1 ≤ N ≤ 10^{5}$
$0 ≤ K ≤ N$
- Sum of $N$ over all test cases does not exceed $2 \cdot 10^{5}$

----- Sample Input 1 ------ 
3
8 3
00010111
5 1
10100
6 2
111000

----- Sample Output 1 ------ 
0
2
3

----- explanation 1 ------ 
Test case 1: We are allowed to perform at most $3$ operations. We can perform the following operation on $S$: $0001\underline{0}111 \rightarrow 00011111$ which has $0$ inversions. Therefore $0$ is the answer.

Test case 2: We can perform the following operation on $S$: $\underline{1}0100 \rightarrow 00100$ which has $2$ inversions. It can be proven that this is the minimum number of inversions possible.

Test case 3: We can perform the following operations on $S$: $1110\underline{0}0 \rightarrow 11101\underline{0} \rightarrow 111011$ which has $3$ inversions. It can be proven that this is the minimum number of inversions possible.