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.strip.split.map(&:to_i)
s = gets.strip.split('')

rl = []
count = 0
c = s.first
s.each do |cc|
  if c==cc
    count+=1
  else
    rl << count
    count=1
    c=cc
  end
end
rl << count

if rl.length < k*2+1
  p rl.inject(:+)-1
  exit
end

tmp_result = tmp_index = 0
arrf = rl[0...k*2+1]
current = arrf.inject(:+)
pre_first = rl.first
#p arrf

rl.each_cons(k*2+1).with_index do |arr, i|
  unless i.zero?
    p_c = current
    current -= pre_first
    current += arr.last
    pre_first = arr.first
    next if p_c > current
  end
  tmp_result, tmp_index = current, i if current > tmp_result
  #p [current, arr]
end

rl[tmp_index..tmp_index+k*2] = [tmp_result]
#p rl
#p"---"

result = rl.inject(:+)-rl.length
p result