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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Diagnostics;

class Myon
{
    public Myon() { }
    public static int Main()
    {
        new Myon().calc();
        return 0;
    }

    Scanner cin;
    Func cin2;
    void calc()
    {
        cin = new Scanner();
        cin2 = new Func();
        int[] NK=cin.ArrayInt(2,0);
        int n=NK[0];
        int k=NK[1];
        char[] s=cin.next().ToCharArray();
        List<int> x = new List<int>();
        int ans=0;
        int m=1;
        bool renzoku=false;
        for(int i=0;i<n-1;i++)
        {
            if(renzoku==false&&s[i]==s[i+1]){m++;renzoku=true;}
            else if(renzoku==true&&s[i]==s[i+1]){m++;}
            else if(renzoku==true&&s[i]!=s[i+1]){x.Add(m);m=1;renzoku=false;}
            else x.Add(m);
        }
        x.Add(m);
        for(int i=0;i<k;i++)
        {
            if(x.Count==1)break;
            if(x.Count==2)
            {
                int a=x[x.Count-1];
                x.RemoveAt(x.Count-1);
                x[x.Count-1]+=a;
            }
            else
            {
                int a=x[x.Count-1];
                x.RemoveAt(x.Count-1);
                a+=x[x.Count-1];
                x.RemoveAt(x.Count-1);
                x[x.Count-1]+=a;
            }
        }
        foreach(int i in x)
        {
            ans+=(i-1);
        }
        Console.WriteLine(ans);
    }
}



class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}

class Answer
{
    public void Int2DArrayAns(int[,]x,char c)
    {
        for(int i=0;i<x.GetLength(0);i++)
        {
            for(int j=0;j<x.GetLength(1)-1;j++)
            {
                Console.Write(x[i,j]);
                Console.Write(c);
            }
            Console.WriteLine(x[i,x.GetLength(1)-1]);
        }
    }
    public void Char2DArrayAns(char[,]x,char c)
    {
        for(int i=0;i<x.GetLength(0);i++)
        {
            for(int j=0;j<x.GetLength(1)-1;j++)
            {
                Console.Write(x[i,j]);
                Console.Write(c);
            }
            Console.WriteLine(x[i,x.GetLength(1)-1]);
        }
    }
}

class Func
{
    public long GCDLong(long a, long b)
    {
        while(a!=0)
        {
          long t=a;
          a=b%a;
          b= t;
        }
      
        return b;        
    }
}