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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import scala.io.StdIn
object Main extends App {
  def encodeDirect[X](l: List[X]): List[(Int, X)] = {
    def _encodeDirect(res: List[(Int, X)], rem: List[X]): List[(Int, X)] = rem match {
      case Nil => res
      case ls => {
        val (s, r) = rem span { _ == rem.head }
        _encodeDirect(res:::List((s.length, s.head)), r)
      }
    }
    _encodeDirect(List(), l)
  }
  val List(n,k) = StdIn.readLine().split(" ").map(_.toInt).toList
  val S = StdIn.readLine()
  println((n-1).min(encodeDirect(S.toList).foldLeft(0)((z, n) => z + 0.max(n._1-1)) + 2 * k))
}