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)

input = gets.chomp
a = input.split(' ')
n = a[0].to_i
k = a[1].to_i
s = gets.chomp

# Kが1回前提
d_max_score = 0

for d in 1..k
  for l in 1...n
    for r in l...n
      # p s[l..r], [l,r]
      moved = s.dup
      for z in l..r
        if s[z] == 'L'
          moved[z] = 'R'
        elsif s[z] == 'R'
          moved[z] = 'L'
        end
      end
      ### p [l, r]
      ### p s.dup
      # p moved
      # score 計算
      score = 0
      prev = nil
      for i in 1...moved.size
        if moved[i - 1] == moved[i]
          score += 1
        end

        prev = moved[i]
      end

      if d_max_score < score
        d_max_score = score
      end
    end
  end
end
p d_max_score