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.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ABC140.D();
        }

        class ABC140
        {
            public static void A()
            {
                var N = Read.Int();
                Console.WriteLine(N * N * N);
            }
            public static void B()
            {
                var N = Read.Int();
                var A = Read.IntN();
                var B = Read.IntN();
                var C = Read.IntN();
                long sum = B.Sum();
                for(int i = 0; i < N - 1; ++i)
                {
                    if (A[i] + 1 == A[i + 1])
                    {
                        sum += C[A[i] - 1];
                    }
                }
                Console.WriteLine(sum);
            }
            public static void C()
            {
                var N = Read.Int();
                var B = Read.IntN();
                var A = new long[N];
                A[0] = B[0];
                A[N - 1] = B[N - 2];
                for (int i = 1; i < N - 1; ++i)
                {
                    A[i] = Math.Min(B[i - 1], B[i]);
                }
                Console.WriteLine(A.Sum());
            }
            public static void D()
            {
                var N = Read.Int();
                var K = Read.Int();
                var S = Read.Str();
                int count = 0;
                for(int i = 0; i < N - 1; ++i)
                {
                    count += S[i] != S[i + 1] ? 1 : 0;
                }
                Console.WriteLine(N - 1 - Math.Max(0, count - K * 2));
            }
            public static void E()
            {
                //var N = Read.Int();
                //var P = Read.IntN();

                //var indices = new int[N + 1];

                //for (int i = 0; i < N; ++i)
                //{
                //    indices[P[i]] = i;
                //}

                //var largeIdx = new Util.MultiSet<int>();

                //long sum = 0;
                //largeIdx.Insert(-1);
                //largeIdx.Insert(-1);
                //largeIdx.Insert(N);
                //largeIdx.Insert(N);

                //for (int i = N; i > 0; --i)
                //{
                //    var idx = indices[i];
                //    largeIdx.Insert(idx);
                //    var std = largeIdx.LowerBound(idx);
                //    var idxM2 = largeIdx.ElementAt(Math.Max(0, std - 2));
                //    var idxM1 = largeIdx.ElementAt(Math.Max(0, std - 1));
                //    var idxP1 = largeIdx.ElementAt(Math.Min(largeIdx.Count() - 1, std + 1));
                //    var idxP2 = largeIdx.ElementAt(Math.Min(largeIdx.Count() - 1, std + 2));
                //    sum += ((long)(idxM1 - idxM2) * (idxP1 - idx) + (long)(idx - idxM1) * (idxP2 - idxP1)) * i;
                //}
                //Console.WriteLine(sum);
            }
            public static void F()
            {

            }
        }

        class Util
        {

        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN(); dict[ab[0]].Add(ab[1]);
                    if (!isDirectional) { dict[ab[1]].Add(ab[0]); }
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}