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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ProblemD
{
    class Program
    {
        static void Main(string[] args)
        {
            var read= Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var N = read[0];
            var K = read[1];

            var S = Console.ReadLine().ToCharArray();
            var convertedS = new List<int>();
            var from = 0;
            for (int i = 0; i < S.Length - 1; i++)
            {
                if (S[i] != S[i + 1])
                {
                    convertedS.Add(i - from + 1);
                    from = i + 1;
                }
                if(i == S.Length - 2)
                {
                    if (from == S.Length - 1) convertedS.Add(1);
                    else convertedS.Add(i - from + 2);
                }
            }
            Console.WriteLine(GetMaxNum(convertedS, K));

        }

        static int GetMaxNum(List<int> S, int K)
        {
            if(K == 0)
            {
                return S.Sum() - S.Count();
            }
            else if(S.Count() == 1)
            {
                return S[0] - 1;
            }
            else
            {
                return CalcMaxRet(S, K);
            }
        }

        static int CalcMaxRet(List<int> S, int K)
        {
            var maxRet = 0;
            var sCnt = S.Count();
            var temp = 0;
            for (int i = 0; i < S.Count(); i++)
            {
                var tempS = new List<int>();
                var tempRet = 0;
                if (i == 0)
                {
                    var ins = S[0] + S[1];
                    temp = ins;
                    tempS.Add(ins);
                    tempS.AddRange(S.GetRange(2, sCnt - 2));
                    tempRet = GetMaxNum(tempS, K - 1);
                }
                else if(i == sCnt - 1)
                {
                    var ins = S[sCnt - 2] + S[sCnt - 1];
                    if (ins >= temp - 2)
                    {
                        tempS.AddRange(S.GetRange(0, sCnt - 2));
                        tempS.Add(ins);
                        tempRet = GetMaxNum(tempS, K - 1);
                    }
                }
                else
                {
                    var ins = S[i - 1] + S[i] + S[i + 1];
                    temp = Math.Max(ins, temp);
                    if(ins >= temp - 2)
                    {
                        tempS.AddRange(S.GetRange(0, i - 1));
                        tempS.Add(ins);
                        tempS.AddRange(S.GetRange(i + 2, sCnt - i - 2));
                        tempRet = GetMaxNum(tempS, K - 1);
                    }
                }
                maxRet = Math.Max(maxRet, tempRet);
            }
            return maxRet;

        }
    }
}