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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

/**
 * @author Finn Lidbetter
 */
import java.util.*;
import java.io.*;
import java.awt.geom.*;

public class Main {
  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringBuilder sb = new StringBuilder();
    
    String[] s = br.readLine().split(" ");
    int n = Integer.parseInt(s[0]);
    int k = Integer.parseInt(s[1]);
    char[] seq = br.readLine().toCharArray();
    ArrayList<Integer> vals = new ArrayList<>();
    char c = '?';
    int count = 0;
    for (int i=0; i<n; i++) {
      if (c=='?') {
        c = seq[i];
        count = 1;
        continue;
      } else {
        if (seq[i]==c) {
          count++;
        } else {
          c = seq[i];
          vals.add(count);
          count = 1;
        }
      }
    }
    vals.add(count);
    int sum = vals.get(0);
    int index = 1;
    for (int i=0; i<k && index<vals.size(); i++) {
      sum += vals.get(index);
      if (index+1<vals.size())
        sum += vals.get(index+1);
      index += 2;
    }
    int total = sum - 1;
    for (int i=index; i<vals.size(); i++) {
      total += vals.get(i)-1;
    }
    System.out.println(total);
  }
}