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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var input = Console.ReadLine().Split(' ');

        var N = int.Parse(input[0]);
        var K = int.Parse(input[1]);

        var S = Console.ReadLine().ToCharArray();
        var before = "";
        var now = "";
        var ans = 0;
        var single = 0;
        for (var i = 0; i < N; i++)
        {
            now = S[i].ToString();

            if(now == "L" && before == "R")
            {
                ans += 2;
            }

            if(i == 0 && now == "L")
            {
                ans += 1;
                single += 1;
            }

            if(i == N - 1 && now == "R")
            {
                ans += 1;
                single += 1;
            }

            before = now;

        }

        ans = ans - (K - single) * 2;

        if(ans == single)
        {
            ans = 0;
        }
        else if(ans > single)
        {
            ans = ans - single * 2;
        }
        else
        {
            ans = 0;
        }


        Console.WriteLine(N - ans);
        Console.ReadLine();
    }


}