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;
int main(){
  int n,k;
  cin >> n >> k;
  string s;
  cin >> s;
  string t=s;
  int cntl=0;
  bool c=false;
  for(int i=0;i<n;i++){
    if(s[i]==s[0]){
      c=false;
      continue;
    }
    else{
      if(!c){
        if(cntl==k){
          break;
        }
        cntl++;
      }
      c=true;
      s[i]=s[0];
    }
  }
  int ansl=0;
  for(int i=0;i<n-1;i++){
    if(s[i]==s[i+1]){
      ansl++;
    }
  }
  s=t;
  int cntr=0;
  c=false;
  for(int i=n-1;i>=0;i--){
    if(s[i]==s[n-1]){
      c=false;
      continue;
    }
    else{
      if(!c){
        if(cntr==k){
          break;
        }
        cntr++;
      }
      c=true;
      s[i]=s[n-1];
    }
  }
  int ansr=0;
  for(int i=0;i<n-1;i++){
    if(s[i]==s[i+1]){
      ansr++;
    }
  }
  cout << max(ansl,ansr) << endl;
}