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.Linq;

class Program
{
    static void Main()
    {
        var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var N = input[0];
        var K = input[1];
        var S = Console.ReadLine().ToCharArray();

        var index = 0;
        var j = 0;
        for (var i = 0; i < K; i++)
        {
            index = Array.IndexOf(S, S[0] == 'R' ? 'L' : 'R');

            if (index == -1)
            {
                break;
            }
            j = index;
            while (S[j] != S[0])
            {
                S[j] = S[0];
                j++;
                if (j >= S.Length)
                {
                    break;
                }
            }
        }

        var result = 0;
        for (int i = 1; i < N; i++)
        {
            if (S[i - 1] == S[i])
            {
                result++;
            }
        }
        Console.WriteLine(result);
    }
}