1690D · Black and White Stripe

Problem: You have a stripe of checkered paper of length $n$. Each cell is either white or black.

What is the minimum number of cells that must be recolored from white to black in order to have a segment of $k$ consecutive black cells on the stripe?

If the input data is such that a segment of $k$ consecutive black cells already exists, then print 0.

Input Format: The first line contains an integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

Next, descriptions of $t$ test cases follow.

The first line of the input contains two integers $n$ and $k$ ($1 \le k \le n \le 2\cdot10^5$). The second line consists of the letters 'W' (white) and 'B' (black). The line length is $n$.

It is guaranteed that the sum of values $n$ does not exceed $2\cdot10^5$.

Output Format: For each of $t$ test cases print an integer — the minimum number of cells that need to be repainted from white to black in order to have a segment of $k$ consecutive black cells.

Note: In the first test case, $s$="BBWBW" and $k=3$. It is enough to recolor $s_3$ and get $s$="BBBBW". This string contains a segment of length $k=3$ consisting of the letters 'B'.

In the second test case of the example $s$="BBWBW" and $k=5$. It is enough to recolor $s_3$ and $s_5$ and get $s$="BBBBB". This string contains a segment of length $k=5$ consisting of the letters 'B'.

In the third test case of the example $s$="BBWBW" and $k=1$. The string $s$ already contains a segment of length $k=1$ consisting of the letters 'B'.