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)

nn, kk = gets.split.map(&:to_i)
ss = gets.chomp

if nn==1
  puts 0
  exit
end

sum = 0
prev = 'R'
c1 = ss[0]=='R' ? 'R' : 'L'
c2 = ss[0]=='R' ? 'L' : 'R'

# 最後以外カウント
0.upto(nn-2) do |n|
  if ss[n]=='R' && ss[n+1]=='R'
    sum+=1
  elsif ss[n]=='L' && prev=='L'
    sum+=1
  end
  prev = ss[n]
end
# 最後
if ss[-1]=='L' && ss[-2]=='L'
  sum+=1
end

#RLの数
cnt = ss.scan(/#{c1}#{c2}/).size

#補正
edge_cnt = 0
if ss[0]=='R'
  if ss[-1]=='L'
    cnt-=1
    edge_cnt+=1
  end
else #ss[0]=L
  if ss[-1]=='R'
    cnt-=1
    edge_cnt+=1
  end
end
inc = 0

if cnt >= kk
  inc = kk*2
else
  kk -= cnt
  inc = cnt * 2 + [kk,edge_cnt].min
end
puts sum + inc