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Sorting the Pieces - Repovive Starter Round 7 | Repovive

21F. Sorting the Pieces

3000 pts2s256 MB

You are given a string $s$ consisting of lowercase English letters and an integer $k$ .

You may choose at most $k$ pairwise disjoint substrings of $s$ . For each chosen substring, independently rearrange its characters into nondecreasing alphabetical order.

Your goal is to make the entire string $s$ sorted in nondecreasing alphabetical order.

Find the minimum possible sum of the lengths of the chosen substrings. If $s$ is already sorted, you may choose no substrings, with a total length of $0$ .

Constraints

$1 \le t \le 10^4$
$1 \le n \le 2 \times 10^5$
$1 \le k \le n$
The sum of $n$ over all test cases is at most $2 \times 10^5$
$s$ consists only of lowercase English letters

Input

The first line contains the number of test cases $t$ .

Each test case is given in the following format:

\left. \begin{array}{l} n \quad k \\ s \end{array} \right\} \times t

Output

For each test case, output one integer: the minimum possible sum of the lengths of the chosen substrings.

\left. \begin{array}{l} ans \end{array} \right\} \times t

Samples

Input

Case 1

9 1
bacdehgfi

Case 2

9 2
bacdehgfi

Explanation

Case 1

Sorting positions $1$ through $8$ produces the sorted string abcdefghi, with total length $8$ . The letters at positions $1$ and $2$ must exchange places, and so must the letters at positions $6$ and $8$ . With only one chosen substring, it has to cover all positions from $1$ through $8$ .

Case 2

Sort the substring at positions $1$ through $2$ and the substring at positions $6$ through $8$ . Their total length is $2+3=5$ , and every position that changes is covered.

Output

Case 1

Case 2

Input

Case 1

5 2
edcba

Case 2

14 2
bacdgfehijknml

Case 3

14 3
bacdgfehijknml

Explanation

Case 1

Sorting the whole string gives abcde, with cost $5$ . The letters a and e have to move between the two ends, so no shorter chosen substring can be sufficient.

Case 2

Sort positions $1$ through $7$ and positions $12$ through $14$ . The resulting string is abcdefghijklmn, and the total length is $7+3=10$ . With only two substrings, at least two of the three separated unsorted parts must be covered together; joining the first two has the smallest cost.

Case 3

Sort positions $1$ through $2$ , positions $5$ through $7$ , and positions $12$ through $14$ . These substrings have total length $2+3+3=8$ and make the whole string sorted.

Output

Case 1

Case 2

Case 3

You are given a string $s$ consisting of lowercase English letters and an integer $k$ .

You may choose at most $k$ pairwise disjoint substrings of $s$ . For each chosen substring, independently rearrange its characters into nondecreasing alphabetical order.

Your goal is to make the entire string $s$ sorted in nondecreasing alphabetical order.

Find the minimum possible sum of the lengths of the chosen substrings. If $s$ is already sorted, you may choose no substrings, with a total length of $0$ .

$1 \le t \le 10^4$
$1 \le n \le 2 \times 10^5$
$1 \le k \le n$
The sum of $n$ over all test cases is at most $2 \times 10^5$
$s$ consists only of lowercase English letters

The first line contains the number of test cases $t$ .

Each test case is given in the following format:

\left. \begin{array}{l} n \quad k \\ s \end{array} \right\} \times t

For each test case, output one integer: the minimum possible sum of the lengths of the chosen substrings.

\left. \begin{array}{l} ans \end{array} \right\} \times t

Sort the substring at positions $1$ through $2$ and the substring at positions $6$ through $8$ . Their total length is $2+3=5$ , and every position that changes is covered.

Sorting the whole string gives abcde, with cost $5$ . The letters a and e have to move between the two ends, so no shorter chosen substring can be sufficient.

Sort positions $1$ through $2$ , positions $5$ through $7$ , and positions $12$ through $14$ . These substrings have total length $2+3+3=8$ and make the whole string sorted.

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21F. Sorting the Pieces

Constraints

Input

Output

Samples

21F. Sorting the Pieces

Constraints

Input

Output

Samples