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;

class Program
{
    static void Main(string[] args)
    {

        //スペース区切りの整数の入力
        string[] input = Console.ReadLine().Split(' ');
        int n = int.Parse(input[0]);
        int k = int.Parse(input[1]);

        string s = Console.ReadLine();
        char[] c = s.ToCharArray();

        List<int> result = returnNumList(c);

        if (result.Count <= 2*k+1)
        {
            Console.WriteLine(n-1);
            return;
        }

        for (int x = 0; x < k; x++)
        {
            int[] sum = new int[result.Count-2];
            int maxsum = 0;
            int maxsum_index = -1;
            for (int y = 0;y< result.Count - 2; y++)
            {
                sum[y] = result[y] + result[y+1] + result[y+2];
                if (sum[y] > maxsum)
                {
                    maxsum = sum[y];
                    maxsum_index = y;
                }
            }

            result.RemoveAt(maxsum_index);
            result.RemoveAt(maxsum_index);
            result.RemoveAt(maxsum_index);
            result.Insert(maxsum_index, maxsum);
        }

        


        Console.WriteLine(n-result.Count);
        return;
    }

    static List<int> returnNumList(char[] c)
    {
        List<int> result = new List<int>();
        int tmp = 1;
        if (c.Length == 1)
        {
            result.Add(1);
            return result;
        }
        for (int i = 0; i < c.Length; i++)
        {
            if (i == c.Length - 1)
            {
                    result.Add(tmp);
                    return result;
            }
            if (c[i] == c[i + 1])
            {
                tmp++;
            }
            else
            {
                result.Add(tmp);
                tmp = 1;
            }
        }
        return result;
    }

}