Problem Statement

For a string $T$ consisting of lowercase English letters, consider the question below, and let $f(T)$ be the answer.

Find the number of different strings obtained by performing the following operation any number of times: delete the first character from $T$ and append it to the end.

You are given a string $S$ of length $N$ consisting of lowercase English letters. You can perform the operation below at most $K$ times (possibly zero).

• Choose a character of $S$ and change it to any lowercase English letter.

Find the minimum possible value of $f(S)$ after your operations.

Constraints

• $1 \\le N \\le 2000$
• $0 \\le K \\le N$
• $S$ is a string of length $N$ consisting of lowercase English letters.
• $N$ and $K$ are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$ $S$

Output

Print the answer.

Sample Input 1

4 1
abac

Sample Output 1

2

If you change the fourth character c to b in the first operation, you get $S=$ abab, with $f(S)=2$.

$f(S)$ cannot be made $1$ or less in one or fewer operations, so the answer is $2$.

Sample Input 2

10 0
aaaaaaaaaa

Sample Output 2

1

Sample Input 3

6 1
abcaba

Sample Output 3

3