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 Fortran (GNU Fortran 9.2.1) (judge verdict: Accepted)

program prob6
    implicit none
    integer :: N, K, i, a, b, ans
    character(100005) :: S
    read(*,*) N, K, S
    
    ans = 0
    do i = 2, N-1
        if(S(i:i) == 'L')then
            if(S(i-1:i-1) == 'L')then
                ans = ans + 1
            end if
        end if
        if(S(i:i) == 'R')then
            if(S(i+1:i+1) == 'R')then
                ans = ans + 1
            end if
        end if
    end do
    if(S(1:1) == 'R')then
        if(S(2:2) == 'R')then
            ans = ans + 1
        end if
    end if
    if(S(N:N) == 'L')then
        if(S(N-1:N-1) == 'L')then
            ans = ans + 1
        end if
    end if

    a = 0
    b = 0
    do i = 1, N-1
        if(S(i:i) == 'L' .and. S(i+1:i+1) == 'R')then
            a = a + 1
        end if
        if(S(i:i) == 'R' .and. S(i+1:i+1) == 'L')then
            b = b + 1
        end if
    end do
    ans = ans + 2 * min(a, min(b, K))
    if(K > min(a, b)) then
        ans = ans + K - min(a, b)
    end if
    ans = min(ans, N-1)

    write(*,*) ans

    stop
contains
end program prob6