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: Wrong Answer)

n, k = gets.chomp.split.map(&:to_i)
s = gets.chomp.split('')

def count(a)
  sum = 0
  asize = a.size
  asize.times do |i|
    sum += 1 if (a[i] == 'L' && i != 0 && a[i - 1] == 'L') || (a[i] == 'R' && i != asize - 1 && a[i + 1] == 'R')
  end
  sum
end

def shuffle(a, l, r)
  first, middle, last = a[0...l-1], a[l-1..r-1], a[r..a.size]
  middle.reverse!
  middle = middle.map do |c|
    if c == 'R'
      'L'
    else
      'R'
    end
  end
  first + middle + last
end

max = 0

queue = []
queue.push([s, 0, 0])
while !queue.empty?
  s, l, r = queue.shift
  if l != 0 && r != 0
    suffled = shuffle(s, l, r)
  else
    suffled = s
  end
  num = count(suffled)
  max = num if num > max
  k -= 1
  if k >= 0
    (1..n).to_a.repeated_permutation(2) do |ll, rr|
      queue.push([suffled, ll, rr]) if ll < rr
    end
  end
end
p max