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;
typedef vector<int> vi;
typedef pair<int,int> pii;
typedef long long ll;
const long long MOD=1e09+7;



#define rep(i,n) for(int i=0;i<n;i++)
#define rep2(i,m,n) for(int i=m;i<n;i++)
#define ALL(v) v.begin(), v.end()
#define pb push_back



      






int main(){
 
  int n,k;
  cin>>n>>k;
  string s;
  cin>>s;
  
  int count=0;
  rep(i,n){
    if (s.at(i)=='L'){
      if (i>=1 and s.at(i-1)=='L'){
        count++;
      }
    }
    else {
      if (i<=n-2 and s.at(i+1)=='R'){
        count++;
      }
    }
  }
  
  rep(i,k){
    count=min(count+2,n-1);
  }
  
  cout<<count<<endl;
  

}