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.Collections.Generic;
using System.Linq;
    class Program
    {
        static void Main(string[] args)
        {
            string line1 = Console.ReadLine();
            string line2 = Console.ReadLine();
            
            int N = int.Parse(line1.Split(' ')[0]);
            int K = int.Parse(line1.Split(' ')[1]);
            //string S = line2;

            char[] C = line2.ToCharArray();
            List<string> S = new List<string>(C.Select((arg) => arg.ToString()));

            int point = 0;

            S = Re(S,K,1);
            foreach(string s in S)
            {
                Console.Write(s + " ");
            }
        }

        static List<string> Re(List<string> S,int limit,int count)
        {
            int LRindex = 0;
            int RLindex = 0;

            if (count <= limit)
            {

                for (int i = 0; i < S.Count; i++)
                {
                    if (i + 1 < S.Count)
                    {
                        if (S[i] == "L" && S[i + 1] == "R")
                        {
                            LRindex = i;
                        }
                    }
                }

                for (int i = 0; i < S.Count; i++)
                {
                    if (i + 1 < S.Count)
                    {
                        if (S[i] == "R" && S[i + 1] == "L" && (i + 1 != LRindex || LRindex + 1 != i))
                        {
                            RLindex = i;
                        }
                    }
                }

                if (RLindex != 0 && LRindex != 0)
                {

                    if (LRindex < RLindex)
                    {
                        for (int i = LRindex; i < RLindex; i++)
                        {
                            if (S[i + 1] == "R")
                            {
                                S[i + 1] = "L";
                            }
                            else
                            {
                                S[i + 1] = "R";
                            }
                        }
                    }
                    else if (LRindex > RLindex)
                    {
                        for (int i = RLindex; i < LRindex; i++)
                        {
                            if (S[i + 1] == "R")
                            {
                                S[i + 1] = "L";
                            }
                            else
                            {
                                S[i + 1] = "R";
                            }
                        }
                    }

                    Re(S,limit,count+1);
                }
                else if (RLindex == 0)
                {
                    for (int i = 0; i <= LRindex; i++)
                    {
                        S[i] = "R";
                    }
                }
                else if (LRindex == 0)
                {
                    for (int i = 0; i <= RLindex; i++)
                    {
                        S[i] = "L";
                    }
                }

                return S;
            }
            else
            {
                return S;
            }
        }
    }