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)

require 'pp'
n,k = gets.split.map(&:to_i)
s = gets.chomp.chars
# p s
ss = s.map.with_index{|s,i|[s,i]}.chunk_while{|a,b|a[0] == b[0]}.map{|a|a.size * (a[0][0] == "R" ? 1 : -1)}.to_a
# 3 9 9 7
# p k
# p ss
# p ss.map(&:abs).each_cons(2).map{|x|x.inject(:+)}
# p ss.map(&:abs).each_cons(2).map{|x|x.inject(:+)}.max(k).inject(:+)
arr = []
sss = ss
sss[-1] = sss[-1] - 1
arr << ss.map(&:abs).each_cons(2).map{|x|x.inject(:+)}.max(k).inject(:+)


sss = ss
sss[0] = sss[0] - 1
arr << ss.map(&:abs).each_cons(2).map{|x|x.inject(:+)}.max(k).inject(:+)
p arr.min