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;

public class ABC0140_A4v1 {
    private static void Main(string[] args) {
        var inputs = new List<string>() {
            Console.ReadLine().Trim(),
            Console.ReadLine().Trim(),
        };

        Prepare(inputs);
    }

    private static void Prepare(List<string> inputs) {
        var ints = inputs[0].Split().Select(x => int.Parse(x)).ToArray();
        var numOfDirections = ints[0];
        var numOfTrials = ints[1];
        var directions = inputs[1];
        Compute(numOfDirections, numOfTrials, directions);
    }

    private static void Compute(int numOfDirections, int numOfTrials, string directions) {
        var initialHappiness = 0;

        for (var index = 0; index < numOfDirections - 1; index++) {
            if (directions[index] == directions[index + 1])
                initialHappiness++;
        }

        var happiness = initialHappiness + (2 * numOfTrials);

        if (happiness > numOfDirections - 1) {
            if ((numOfDirections - initialHappiness) % 2 == 0)
                happiness = numOfDirections;
            else
                happiness = numOfDirections - 1;
        }

        OutputAnswer(happiness.ToString());
    }

    private static void OutputAnswer(string text) => Console.WriteLine(text);
}