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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n,k = gets.chomp.split(" ").map(&:to_i)
s = gets.chomp.split("").map{|c| c == "L" ? -1 : 1}

k.times do
  index = -1
  tmp_arr = []
  lr = s[0]
  (0..s.length-1).each do |i|
    next if s[i] == lr
    index = i
    tmp_arr << s[i]
    (i+1..s.length-1).each do |j|
      if s[j] == lr then
        break
      else
        tmp_arr << s[j]
      end
    end
    break
  end
  break if index == -1
  length = tmp_arr.length
  tmp_arr.each_with_index do |c, i|
    s[index+length-1-i] = c * (-1)
  end
end

count = 0
s.each_cons(2) do |c1, c2|
  count += 1 if c1 == c2
end
puts count