Problem:
Score : 400 points

Problem Statement

There are N people standing in a queue from west to east.

Given is a string S of length N representing the directions of the people.
The i-th person from the west is facing west if the i-th character of S is L, and east if that character of S is R.

A person is happy if the person in front of him/her is facing the same direction.
If no person is standing in front of a person, however, he/she is not happy.

You can perform the following operation any number of times between 0 and K (inclusive):

Operation: Choose integers l and r such that 1 \leq l \leq r \leq N, and rotate by 180 degrees the part of the queue: the l-th, (l+1)-th, ..., r-th persons. That is, for each i = 0, 1, ..., r-l, the (l + i)-th person from the west will stand the (r - i)-th from the west after the operation, facing east if he/she is facing west now, and vice versa.

What is the maximum possible number of happy people you can have?

Constraints

N is an integer satisfying 1 \leq N \leq 10^5.

K is an integer satisfying 1 \leq K \leq 10^5.

|S| = N

Each character of S is L or R.

Input

Input is given from Standard Input in the following format:

N K
S

Output

Print the maximum possible number of happy people after at most K operations.

Sample Input 1

6 1
LRLRRL

Sample Output 1

3

If we choose (l, r) = (2, 5), we have LLLRLL, where the 2-nd, 3-rd, and 6-th persons from the west are happy.

Sample Input 2

13 3
LRRLRLRRLRLLR

Sample Output 2

9

Sample Input 3

10 1
LLLLLRRRRR

Sample Output 3

9

Sample Input 4

9 2
RRRLRLRLL

Sample Output 4

7

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let () =
    let main () =
        let n, k = Scanf.sscanf (read_line ()) "%d %d" (fun n k -> n, k) in
        let s = read_line () in
        let rec loop i prev acc =
            if i = n then acc else
                if prev = s.[i] then loop (i + 1) s.[i] acc else
                        loop (i + 1) s.[i] (acc + 1)
        in
        let a = loop 1 s.[0] 0 in
        let rest_k = k - min (a / 2) k in
        let rest_a = a - 2 * (k - rest_k) in
        let rest_a = if rest_a = 1 && rest_k > 0 then rest_a - 1 else rest_a in

        let r = n - (rest_a + 1) in
        Printf.printf "%d\n" r
    in
    main ()