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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static System.Math;
using static System.Console;


class Program
{
    static long[] sizes = new long[51];

    public class Tree
    {
        public class Node
        {
            public int? Parent = null;
            public List<int[]> Children = new List<int[]>();
            public int ParentColor = -1;
        }

        public Tree(int nodeNumber)
        {
            Nodes = new Node[nodeNumber];
            for (int i = 0; i < Nodes.Length; i++)
            {
                Nodes[i] = new Node();
                Connenters = new List<int[]>();

            }
        }

        /// <summary>
        /// 頂点の配列。それぞれの頂点には、一つの親と、複数の子がある
        /// </summary>
        public Node[] Nodes { get; }

        public List<int[]> Connenters { get; }

        public void Connent(int to ,int from,int id = -1)
        {
            Connenters.Add(new int[3] { to, from, 0 });
            Nodes[to].Children.Add(new int[2] {from,id });
            Nodes[from].Parent = to;
        }


    }

    static void Main()
    {
        int[] NK = ReadIntN();
        int K = NK[1];
        string S = ReadStr();
        List<int[]> states = new List<int[]>();
        int[] previous = { -1,-1};
        int count = 0;
        for (int i = 0; i < S.Length; i++)
        {
            int state = S[i] == 'R' ? 1 : 0;

            if (previous[0] == state) previous[1]++;
            else
            {
                states.Add(new int[2] { previous[0], previous[1] });
                count += previous[1] - 1;
                previous = new int[2] { state, 1 };
            }
        }
        states.RemoveAt(0);
        count+=2;
        states.Add(previous);
        count += previous[1]-1;
        

        if ((states.Count - 1) / 2 >= K) count += 2 * K;
        else count += states.Count - 1;
        WriteLine(count);
        ReadLine();
    }

    static long F(long N,long X)
    {
        if (X == 1 && N == 0) return 1;
        else if (X == 1) return 0;
        else if (X > 1 && X < sizes[N] / 2 + 1) return F(N - 1, X - 1);
        else if (X == sizes[N] / 2 + 1) return F(N - 1, sizes[N - 1]) + 1;
        else if (X > sizes[N] / 2 + 1 && X < sizes[N])
        {
            return F(N - 1, sizes[N - 1]) + 1 + F(N - 1, X - (sizes[N] / 2 + 1));
        }
        else return 2 * F(N - 1, sizes[N - 1]) + 1;

    }

    #region Reader
    static string ReadStr()
    {
        return Console.ReadLine();
    }
    static string[] ReadStrN()
    {
        return Console.ReadLine().Split(' ');
    }
    static int ReadInt()
    {
        return Convert.ToInt32(Console.ReadLine());
    }
    static int[] ReadIntN()
    {
        return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray();
    }
    static long ReadLong()
    {
        return Convert.ToInt64(Console.ReadLine());
    }
    static long[] ReadLongN()
    {
        return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray();
    }
    static long[,] ReadLongMatrix(int r, int c)
    {
        var mat = new long[r, c];
        for (int i = 0; i < r; ++i)
        {
            var x = ReadLongN();
            for (int j = 0; j < c; ++j)
            {
                mat[i, j] = x[j];
            }
        }
        return mat;
    }
    static Tuple<string, string>[] ReadTupleStr(int n)
    {
        List<Tuple<string, string>> list = new List<Tuple<string, string>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadStrN();
            list.Add(new Tuple<string, string>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<long, long>[] ReadTupleLong(int n)
    {
        List<Tuple<long, long>> list = new List<Tuple<long, long>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadLongN();
            list.Add(new Tuple<long, long>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<int, int>[] ReadTupleInt(int n)
    {
        List<Tuple<int, int>> list = new List<Tuple<int, int>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadIntN();
            list.Add(new Tuple<int, int>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<double, double>[] ReadTupleDouble(int n)
    {
        List<Tuple<double, double>> list = new List<Tuple<double, double>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadLongN();
            list.Add(new Tuple<double, double>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Dictionary<int, HashSet<int>> ReadAdjacencyList(int N, int M)
    {
        Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
        for (int i = 0; i <= N; ++i)
        {
            dict.Add(i, new HashSet<int>());
        }
        for (int i = 0; i < M; ++i)
        {
            var ab = ReadIntN();
            dict[ab[0]].Add(ab[1]);
            dict[ab[1]].Add(ab[0]);
        }
        return dict;
    }
    #endregion
}