Complete Word

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 ≤ i ≤ n;
• s has a period of k, i.e. s_i=s_{k+i} for all 1 ≤ i ≤ 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 ≤ i ≤ 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 ≤ t≤ 10^5) — the number of test cases.

The first line of each test case contains two integers n and k (1 ≤ k < n ≤ 2 ⋅ 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 ⋅ 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.

Example

Input

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

Output

2 0 23 16

Note

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

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

inputFormat

Input

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

The first line of each test case contains two integers n and k (1 ≤ k < n ≤ 2 ⋅ 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 ⋅ 10^5.

outputFormat

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.

Example

Input

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

Output

2 0 23 16

Note

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

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

样例

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

2
0
23
16

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