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;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	class Pair{
		public int Gain, Rest;
		public Pair(int g, int r){
			Gain = g; Rest = r;
		}
	}
	public void Solve(){
		
		List<int> L = new List<int>();
		int cnt = 1;
		for(int i=1;i<N;i++){
			if(S[i] == S[i-1]){
				cnt++;
			} else {
				L.Add(cnt);
				cnt = 1;
			}
		}
		L.Add(cnt);
		
		int M = L.Count;
		String LR = S[0] == 'L' ? "LR" : "RL";
		
		// into R
		int[] gain = new int[M];
		List<Pair> gs = new List<Pair>();
//Console.WriteLine(String.Join(" ",L));		
//Console.WriteLine(String.Join(" ",gain));		
		int rsc = 0;
		for(int i=0;i<L.Count;i++){
			if(LR[i % 2] == 'R'){
				gain[i] = L[i] - 1;
				rsc += gain[i];
			} else {
				gain[i] = L[i];
				if(i == M - 1) gain[i]--;
				if(i > 0) gain[i]++;
				gs.Add(new Pair(gain[i], L[i] - 1));
			}
		}
		gs.Sort((p, q) => {
			if(p.Gain == q.Gain) return p.Rest.CompareTo(q.Rest);
			else return -1 * p.Gain.CompareTo(q.Gain);
		});
		for(int i=0;i<gs.Count;i++){
			if(i < K) rsc += gs[i].Gain;
			else rsc += gs[i].Rest;
		}
		// into L
		gain = new int[M];
		gs = new List<Pair>();
		
		int lsc = 0;
		for(int i=0;i<L.Count;i++){
			if(LR[i % 2] == 'L'){
				gain[i] = L[i] - 1;
				lsc += gain[i];
			} else {
				gain[i] = L[i];
				if(i == 0) gain[i]--;
				if(i < M - 1) gain[i]++;
				gs.Add(new Pair(gain[i], L[i] - 1));
			}
		}
		gs.Sort((p, q) => {
			if(p.Gain == q.Gain) return p.Rest.CompareTo(q.Rest);
			else return -1 * p.Gain.CompareTo(q.Gain);
		});
		for(int i=0;i<gs.Count;i++){
			if(i < K) lsc += gs[i].Gain;
			else lsc += gs[i].Rest;
		}
		
		//Console.WriteLine("{0} {1}",lsc, rsc);
		Console.WriteLine(Math.Max(lsc, rsc));
	}
	int N,K;
	String S;
	public Sol(){
		var d = ria();
		N = d[0]; K = d[1];
		S = rs();
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}