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;
using System.Text;
using System.Threading.Tasks;




class Program 
{
    const int MOD = 1000000007;
    const int INF = 1 << 30;



    static void Main(string[] args) 
    {
        Solve();
    }



    static void Solve() 
    {
        Scaner cin = new Scaner();
        write cout = new write();
        Math2 mmath = new Math2();
        //ここから
        var o = cin.LongM;
        var N = o[0];
        var K = o[1];
        var S = cin.Str;

        int first = 0;
        for(int i = 0; i < N-1; ++i)
        {
            if (S[i] ==S[i + 1]) first++;
        }
        cout.wri(first);
        cout.wri(Math.Min(first + 2 * K, N - 1));
    }


}






//b-aで降順

    //priority queue
class PriorityQueue<T> 
{
    private readonly List<T> heap;
    private readonly Comparison<T> compare;
    private int size;
    public PriorityQueue() : this(Comparer<T>.Default) {} 
    public PriorityQueue(IComparer<T> comparer) : this(16, comparer.Compare) { }
    public PriorityQueue(Comparison<T> comparison) : this(16, comparison) { }
    public PriorityQueue(int capacity, Comparison<T> comparison)
    {
        this.heap = new List<T>(capacity);
        this.compare = comparison;
    }
    public void Enqueue(T item)
    {
        this.heap.Add(item);
        var i = size++;
        while (i > 0)
        {
            var p = (i - 1) >> 1;
            if (compare(this.heap[p], item) <= 0)
                break;
            this.heap[i] = heap[p];
            i = p;
        }
        this.heap[i] = item;

    }
    public T Dequeue()
    {
        var ret = this.heap[0];
        var x = this.heap[--size];
        var i = 0;
        while ((i << 1) + 1 < size)
        {
            var a = (i << 1) + 1;
            var b = (i << 1) + 2;
            if (b < size && compare(heap[b], heap[a]) < 0) a = b;
            if (compare(heap[a], x) >= 0)
                break;
            heap[i] = heap[a];
            i = a;
        }
        heap[i] = x;
        heap.RemoveAt(size);
        return ret;
    }
    public T Peek() { return heap[0]; }
    public int Count { get { return size; } }
    public bool Any() { return size > 0; }
}


 public class Math2
{
    public long[] Fact;  //Nまでの階乗
    public long[] invFact;  //階乗の逆元

    //Nまでの階乗をセットしておく
    public void FactoricalModSet(long N,long MOD=1000000007)
    {
        Fact = new long[N + 1];
        invFact = new long[N + 1];

        Fact[0] = 1;
        for(long i = 1; i <= N; ++i)
        {
            Fact[i] = Fact[i - 1] * i%MOD;
        }
        invFact[N] = pow(Fact[N], MOD - 2);

        for (long i = N; i > 0; --i)
        {
            invFact[i - 1] = invFact[i] * i%MOD;
        }

    }

    //nCr 引数:n r (mod)
    public long nCr(long n,long r,long MOD=1000000007)
    {
        return (Fact[n] * invFact[r] % MOD * invFact[n-r]%MOD);
    }

    //階乗(O(logN)) 引数:底x n乗　(MOD)
    public long pow(long x,long n,long MOD = 1000000007)
    {
        long res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * x % MOD;
            x = x * x % MOD;
            n >>= 1;
        }
        return res;
    }

    //最大公約数 引数:整数x,y
    public long GCD(long x, long y)
    {
        while (y != 0)
        {
            var r = x % y;
            x = y;
            y = r;
        }
        return x;
    }

    //最小公倍数 引数:整数x,y
    public long LCM(long x, long y)
    {
        return x * y / GCD(x, y);
    }

    //素因数分解 引数:整数N
    public Dictionary<long,int > PrimeFactorization(long N)
    {
        var ret = new Dictionary<long,int>();

        for(long i = 2; i*i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;

        }
        if (N >= 2)ret[N]=1;

        return ret;

    }


}


namespace CompLib.Algorithms
{

    #region BinarySearch
    public static partial class Algorithm
    {
        static int binarySearch<T>(IList<T> a, T v, IComparer<T> cmp, bool islb)
        {
            var l = 0;
            var r = a.Count - 1;
            while (l <= r)
            {
                var m = (l + r) / 2;
                var res = cmp.Compare(a[m], v);
                if (res < 0 || (res == 0 && !islb)) l = m + 1;
                else r = m - 1;
            }
            return l;
        }

        /// <summary>
        /// 与えられた比較関数に従って，<paramref name="a"/> の要素のうち，<paramref name="v"/> 以上の要素であるような最小のインデックスを取得します．
        /// </summary>
        /// <typeparam name="T"><see cref="IList{T}"/> の要素の型を指定します．</typeparam>
        /// <param name="a">対象となるコレクション</param>
        /// <param name="v">対象となる要素</param>
        /// <param name="f"></param>
        /// <returns><paramref name="v"/> 以上の要素であるような最小の o-indexed でのインデックス．</returns>
        /// <remarks> <paramref name="a"/> は比較関数に対して昇順であることを仮定しています．この関数は O(log N) で実行されます．</remarks>
        public static int LowerBound<T>(this IList<T> a, T v, Comparison<T> f) { return binarySearch(a, v, Comparer<T>.Create(f), true); }

        /// <summary>
        ///　デフォルトの比較関数に従って，<paramref name="a"/> の要素のうち，<paramref name="v"/> 以上の要素であるような最小のインデックスを取得します．
        /// </summary>
        /// <typeparam name="T"><see cref="IList{T}"/> の要素の型を指定します．</typeparam>
        /// <param name="a">対象となるコレクション</param>
        /// <param name="v">対象となる要素</param>
        /// <param name="f"></param>
        /// <returns><paramref name="v"/> 以上の要素であるような最小の o-indexed でのインデックス．</returns>
        /// <remarks> <paramref name="a"/> は比較関数に対して昇順であることを仮定しています．この関数は O(log N) で実行されます．</remarks>
        public static int LowerBound<T>(this IList<T> a, T v) { return binarySearch(a, v, Comparer<T>.Default, true); }

        /// <summary>
        /// 与えられた比較関数に従って，<paramref name="a"/> の要素のうち，<paramref name="v"/> 以上の要素であるような最小のインデックスを取得します．
        /// </summary>
        /// <typeparam name="T"><see cref="IList{T}"/> の要素の型を指定します．</typeparam>
        /// <param name="a">対象となるコレクション</param>
        /// <param name="v">対象となる要素</param>
        /// <param name="f"></param>
        /// <returns><paramref name="v"/> 以上の要素であるような最小の o-indexed でのインデックス．</returns>
        /// <remarks> <paramref name="a"/> は比較関数に対して昇順であることを仮定しています．この関数は O(log N) で実行されます．</remarks>
        public static int UpperBound<T>(this IList<T> a, T v, Comparison<T> cmp) { return binarySearch(a, v, Comparer<T>.Create(cmp), false); }

        /// <summary>
        ///　デフォルトの比較関数に従って，<paramref name="a"/> の要素のうち，<paramref name="v"/> より真に大きい要素が現れる最小のインデックスを取得します．
        /// </summary>
        /// <typeparam name="T"><see cref="IList{T}"/> の要素の型を指定します．</typeparam>
        /// <param name="a">対象となるコレクション</param>
        /// <param name="v">対象となる要素</param>
        /// <param name="f"></param>
        /// <returns><paramref name="v"/> 以上の要素であるような最小の o-indexed でのインデックス．</returns>
        /// <remarks> <paramref name="a"/> は比較関数に対して昇順であることを仮定しています．この関数は O(log N) で実行されます．</remarks>
        public static int UpperBound<T>(this IList<T> a, T v) { return binarySearch(a, v, Comparer<T>.Default, false); }

    }
    #endregion
}







class Scaner
{
    public string Str => Console.ReadLine();

    public string[] StrM => Str.Split(' ');

    public long[] LongM => StrM.Select(long.Parse).ToArray();
    public int[] IntM => StrM.Select(int.Parse).ToArray();
    public char[] CharM => Str.ToArray();
    public long Long1 => LongM[0];
    public int Int1 => IntM[0];
    
}



class write
{
    public  void wri<T>(T x)
    {
        Console.WriteLine(x);
    }
}