K-Complete Word

2000ms

524288K

Description:

Word $$$s$$$ of length $$$n$$$ is called $$$k$$$-complete if

$$$s$$$ is a palindrome, i.e. $$$s_i=s_{n+1-i}$$$ for all $$$1 \le i \le n$$$;
$$$s$$$ has a period of $$$k$$$, i.e. $$$s_i=s_{k+i}$$$ for all $$$1 \le i \le n-k$$$.

For example, "abaaba" is a $$$3$$$-complete word, while "abccba" is not.

Bob is given a word $$$s$$$ of length $$$n$$$ consisting of only lowercase Latin letters and an integer $$$k$$$, such that $$$n$$$ is divisible by $$$k$$$. He wants to convert $$$s$$$ to any $$$k$$$-complete word.

To do this Bob can choose some $$$i$$$ ($$$1 \le i \le n$$$) and replace the letter at position $$$i$$$ with some other lowercase Latin letter.

So now Bob wants to know the minimum number of letters he has to replace to convert $$$s$$$ to any $$$k$$$-complete word.

Note that Bob can do zero changes if the word $$$s$$$ is already $$$k$$$-complete.

You are required to answer $$$t$$$ test cases independently.

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t\le 10^5$$$) — the number of test cases.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k < n \le 2 \cdot 10^5$$$, $$$n$$$ is divisible by $$$k$$$).

The second line of each test case contains a word $$$s$$$ of length $$$n$$$.

It is guaranteed that word $$$s$$$ only contains lowercase Latin letters. And it is guaranteed that the sum of $$$n$$$ over all test cases will not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, output one integer, representing the minimum number of characters he has to replace to convert $$$s$$$ to any $$$k$$$-complete word.

Sample Input:

4
6 2
abaaba
6 3
abaaba
36 9
hippopotomonstrosesquippedaliophobia
21 7
wudixiaoxingxingheclp

Sample Output:

Note:

In the first test case, one optimal solution is aaaaaa.

In the second test case, the given word itself is $$$k$$$-complete.

Informação

Provedor Codeforces

Código CF1332C