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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Text;

class Procon {
    static void Main (string[] agrs) {
        int N = Int ();
        int K = Int ();
        char[] S = Chars ();

        int ret = 0;
        int num = 1;
        int tmp = 1;
        for (int i = 0; i < N - 1; i++) {
            if (S[i] == S[i + 1]) {
                tmp++;
            } else {
                ret += tmp - 1;
                tmp = 1;
                num++;
            }
        }
        ret += tmp - 1;

        Console.WriteLine (Math.Min ((ret + K * 2), N - 1));
    }

    static string String () => Scanner.nextString ();
    static int Int () => int.Parse (Scanner.nextString ());
    static long Long () => long.Parse (Scanner.nextString ());
    static double Double () => double.Parse (Scanner.nextString ());
    static char[] Chars () => String ().ToCharArray ();
    static string[] Strings () => Console.ReadLine ().Split (' ');
    static int[] Ints () => Strings ().Select (v => int.Parse (v)).ToArray ();
    static long[] Longs () => Strings ().Select (v => long.Parse (v)).ToArray ();
    static double[] Doubles () => Strings ().Select (v => double.Parse (v)).ToArray ();
    const int M = 1000000007;
}

class PriorityQueue<T> where T : IComparable<T> {
    public T[] heap;
    public int size;
    public int sign;
    public PriorityQueue (int N, bool descend = false) {
        heap = new T[N];
        sign = 1;
        if (descend) sign = -1;
    }
    public int Compare (T x, T y) {
        return x.CompareTo (y) * sign;
    }
    public void Push (T x) {
        int i = size++;
        while (i > 0) {
            int p = (i - 1) / 2;
            if (Compare (x, heap[p]) >= 0) {
                break;
            }
            heap[i] = heap[p];
            i = p;
        }
        heap[i] = x;
    }
    public T Pop () {
        T ret = heap[0];
        T x = heap[--size];
        int i = 0;
        while (i * 2 + 1 < size) {
            int a = i * 2 + 1;
            int b = i * 2 + 2;
            if (b < size && Compare (heap[a], heap[b]) > 0) {
                a = b;
            }
            if (Compare (heap[a], x) >= 0) {
                break;
            }
            heap[i] = heap[a];
            i = a;
        }
        heap[i] = x;
        return ret;
    }
    public int Count () {
        return size;
    }
}

class Scanner {
    static string[] s = new string[0];
    static int i = 0;
    static int max_i = 0;
    static public string nextString () {
        if (i >= s.Length) {
            s = Console.ReadLine ().Split (' ');
            max_i = s.Length;
            i = 0;
            if (max_i == 0) {
                return "";
            }
            return s[i++];
        }
        return s[i++];
    }
}