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;
class Program
{
  static void Main()
  {
    string[] input = Console.ReadLine().Split(' ');
    int N = int.Parse(input[0]);
    int K = int.Parse(input[1]);
    string S = Console.ReadLine();
    
    int hpy = Hpy(S, N);
    int X = 0, Y = 0; // X=(+2できる回数), Y=(+1できる回数)
    
    X = (CountStr(S, "RL") + CountStr(S, "LR")) / 2;
    
    if (S.Substring(0, 1) != S.Substring(S.Length - 1, 1))
    {
      Y = 1;
    }
    
    // 操作
    if (K <= X)
    {
      hpy += K * 2;
    }
    else
    {
      hpy += X * 2 + Y;
    }
    
    Console.WriteLine(hpy);
  }
  
  static int Hpy(string S, int N)
  {
    int buf = 0;
    for (int i = 1; i < N; i++)
    {
      if (S.Substring(i-1, 1) == S.Substring(i, 1))
      {
        buf++;
      }
    }
    return buf;
  }
  
  static int CountStr(string S, string str)
  {
    return (S.Length - S.Replace(str, "").Length) / str.Length;
  }
}