Solve the programming task below in a Python markdown code block.
You are given a binary string S of length N and an integer K. You can perform the following operation on the string:
Select a *prefix* of the string S and flip all the characters of the prefix. A flip corresponds to changing 0 to 1 and vice-versa.

Find the minimum number of operations required to obtain a substring of length K such that all characters of the substring are 1.

Note:
A prefix is obtained by deleting some (possibly zero) characters from the end of the string.
A substring is obtained by deleting some (possibly zero) characters from the beginning of the string and some (possibly zero) characters from the end of the string.

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

- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of multiple lines of input.
- The first line of each test case contains two space-separated integers N and K — the length of the string and the length length of substring containing all 1s we want to achieve.
- The next line contains the binary string S.

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

For each test case, output on a new line, the minimum number of operations required to obtain a substring of length K such that all characters of the substring are 1.

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

$1 ≤ T ≤ 2000$
$1 ≤ K ≤N ≤ 3\cdot 10^{5}$
$S$ consists of $0$ and $1$ only.
- The sum of $N$ over all test cases won't exceed $3\cdot 10^{5}$.

----- Sample Input 1 ------ 
3
3 3
000
4 2
0110
5 3
10101

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

----- explanation 1 ------ 
Test case $1$: We need to obtain a substring containing three $1$s. Using one operation, we can select the prefix $S[1,3]$ and flip all the characters in the prefix. Thus, the string becomes $111$.  

Test case $2$: The string already contains a substring having two $1$s. Thus, we do not need any operation.

Test case $3$: We need to obtain a substring containing three $1$s. We can do so using $2$ operations:
- Operation $1$: Select the prefix $S[1, 4]$ and flip all characters in the prefix. Thus, the string becomes $01011$.
- Operation $2$: Select the prefix $S[1, 3]$ and flip all characters in the prefix. Thus, the string becomes $10111$.

Thus, we have a substring $S[3,5]$ of length $3$ where all characters of the substring are $1$. It can be shown that we cannot obtain such substring using less than $2$ operations.