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: Accepted)

def score(str)
  sr = str.split("L").reject(&:empty?).map { |x| x.count("R") - 1 }.inject(:+)
  sl = str.split("R").reject(&:empty?).map { |x| x.count("L") - 1 }.inject(:+)
  sr.to_i + sl.to_i
end

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

if s.count("L") == n || s.count("R") == n
  puts n - 1
  exit
end

sr = s.split("L").reject(&:empty?)
sl = s.split("R").reject(&:empty?)
if sl.size > sr.size
  # L増やす
  cnt = (k > sr.size ? sr.size : k)
  cnt.times do |i|
    break if sr[i].nil?
    sr[i] = sr[i].gsub!("R", "L")
  end
elsif sl.size < sr.size
  # R増やす
  cnt = (k > sr.size ? sr.size : k)
  cnt.times do |i|
    break if sl[i].nil?
    sl[i] = sl[i].gsub!("L", "R")
  end
else
  cnt = (k > sr.size ? sr.size : k)
  if s[0] == "L"
    cnt.times do |i|
      break if sr[i].nil?
      sr[i] = sr[i].gsub!("R", "L")
    end
  else
    cnt.times do |i|
      break if sl[i].nil?
      sl[i] = sl[i].gsub!("L", "R")
    end
  end
end
ans = []
l_first = (sl.size > sr.size)
if sl.size == sr.size
  l_first = (s[0] == "L")
end
until sl.empty? && sr.empty?
  if l_first
    ans << sl.shift
    l_first = false
  else
    ans << sr.shift
    l_first = true
  end
end
p score(ans.join(""))