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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
class ProgramD
    {
        static void Main(string[] args)
        {

            string[] input = Console.ReadLine().Split(' ');

            int n = int.Parse(input[0]);
            int k = int.Parse(input[1]);

            string s = Console.ReadLine();
            List<int> LR = new List<int>();

            int count = 1;


            for(int i = 1;i < n;i++)
            {
                string si = s.Substring(i, 1);
                string si_p = s.Substring(i-1,1);
                
                if(si != si_p)
                {
                    LR.Add(count);
                    count = 1;
                }
                else
                {
                    count++;
                    if(i == n -1)
                        LR.Add(count);
                }
            }

            long ans = LR.Sum() - LR.Count();
            long LRlen = LR.Count();
            
            for(int i = 0;i < k;i++)
            {
                if(LRlen == 2)
                {
                    ans += 1;
                    break;
                }
                else if((LRlen == 1))
                {
                    break;
                }
                else
                {
                    ans += 2;
                    LRlen -= 2;
                }

            }

            Console.WriteLine(ans);

        }
}