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: Runtime Error)

using System;
using System.Linq;

class D
{
	static void Main()
	{
		var h = Console.ReadLine().Split().Select(int.Parse).ToArray();
		var s = Console.ReadLine();
		int n = h[0], k = h[1];

		var x = Enumerable.Range(1, n - 2).Count(i => s[i] == 'L' ? s[i - 1] == 'L' : s[i + 1] == 'R');
		if (s.StartsWith("RR")) x++;
		if (s.EndsWith("LL")) x++;
		Console.WriteLine(x + Math.Max(Roll(s, n, k, true), Roll(s, n, k, false)));
	}

	static int Roll(string s, int n, int k, bool isL)
	{
		var x = 0;
		var l = s.IndexOf(isL ? 'R' : 'L'); if (l == -1) l = n;
		var r = s.LastIndexOf(isL ? 'R' : 'L');
		var c = isL ? 'L' : 'R';
		for (; k > 0; k--, x += 2, c = c == 'L' ? 'R' : 'L')
		{
			for (; l < r; l++) if (s[l] == c) break;
			for (; l < r; r--) if (s[r] == c) break;
			if (l >= r) break;
		}
		if (k > 0 && s[0] != s[n - 1]) x++;
		return x;
	}
}