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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
   
using namespace std;
     
#define PB(x) push_back(x)
#define ALL(x) (x).begin(), (x).end()
#define ALLR(x) (x).rbegin(), (x).rend()
#define MP(x) make_pair(x);
    
#define debug(x) cerr << #x << '=' << x << endl;
#define debug2(x, y) cerr << #x << '=' << x << ' ' << #y << '=' << y << endl;
#define debugn(a) for (int x: a) cerr << x << ' '; cerr << endl;
     
#define int long long
     
typedef pair<int, int> ii;
typedef vector<int> vi;
typedef vector<pair<int, int>> vii;
typedef vector<string> vs;
typedef unsigned long long ull;

const int INF = 1e13;
const int mmod = 1000000007;

int32_t main()
{	
	int n, k;
	cin >> n >> k;
	string s;
	cin >> s;
	
	int ans = 0;
	for (int i = 1; i < n; i++) {
		if (s[i] == s[i-1]) ans++;
	}
	while (k > 0) {
		ans += 2;
		--k;
	}
	cout << min(n-1, ans) << endl;
	
}