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)

// clang-format off
#include <iostream>
#include <iomanip>
#include <fstream>
#include <sstream>
#include <string>

#include <algorithm>
#include <numeric>
#include <limits>
#include <chrono>
#include <functional>
#include <iterator>
#include <random>
#include <complex>
#include <utility>
#include <type_traits>
#include <tuple>
#include <memory>

#include <vector>
#include <array>
#include <list>
#include <stack>
#include <queue>
#include <deque>
#include <unordered_map>
#include <unordered_set>
#include <map>
#include <set>
#include <valarray>

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <csignal>
#include <cstdint>
#include <cstddef>

#ifdef ONLINE_JUDGE
#define NDEBUG
#endif
#include <cassert>
#include <stdexcept>
#include <exception>

// << pair
template <typename T1, typename T2>std::ostream&operator<<(std::ostream&os,const std::pair<T1,T2>&p){return os<<"("<<p.first<<", "<<p.second<<")";}
// << container
template<typename,template<typename...> class...>struct is_instantiation_of:public std::false_type{};
template<template<typename...>class U,template<typename...>class...Us,typename...T>struct is_instantiation_of<U<T...>,U,Us...>:public std::true_type{};
template<typename S,template<typename...>class U,template<typename...>class...Us>struct is_instantiation_of<S,U,Us...>:std::integral_constant<bool,is_instantiation_of<S,Us...>::value>{};

template<typename C>std::ostream&_debug_go(std::ostream&,const C&);
template<typename C,typename=std::enable_if_t<is_instantiation_of<C,std::vector,std::deque,std::set,std::map,std::unordered_set,std::unordered_map,std::multiset,std::multimap,std::unordered_multiset,std::unordered_multimap,std::valarray>::value>>std::ostream&operator<<(std::ostream&os,const C&v){return _debug_go(os,v);}
template<typename T,std::size_t N> std::ostream& operator<<(std::ostream&os,const std::array<T,N>&v){return _debug_go(os,v);}
template<typename C>std::ostream& _debug_go(std::ostream&os,const C& v){bool first=true;os<<"[";for(auto i:v){if(!first)os<<", ";else first=false;os<<i;}return os<<"]";}

struct Debugger{template<typename T>Debugger&operator,(const T&v){std::cerr<<v<<" ";return *this;}} dbg;
#ifndef NDEBUG
#define debug(args...) do {dbg,args; cerr << "\n";} while(0)
#else
#define debug(args...)
#endif

#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i, 0, n)
#define ITER(i, s, e) for (auto i((s)); i != (e); ++i)
#define IT(i, c) ITER(i, (c).begin(), (c).end())

using namespace std;

using ui = uint32_t;
using ll = int64_t;
using ull = uint64_t;
template <typename T = int> using Pt = complex<T>;

template <typename T>
T cross(const Pt<T>& a, const Pt<T>& b) { return a.real() * b.imag() - a.imag() * b.real(); }

template <typename T>
bool cmpPt(const Pt<T>& a, const Pt<T>& b) {
  return a.real() < b.real() || (a.real() == b.real() && a.imag() < b.imag());
}
// END TEMPLATE
// clang-format on

int solve(int N, int K, const string& S) {
  int ans = 0;
  vector<bool> X(N);
  X[N - 1] = true;
  REP(i, N - 1) ans += !(X[i] = S[i] != S[i + 1]);
  int i = 0, j = 0, ne = 0;
  // debug(i, j, X, ans);
  REP(_, K) {
    while (i < N && !X[i]) ++i;
    if (i == N) break;
    while (j < N && ne != 2) ne += X[j++];
    if (ne != 2) break;
    ne -= 2;
    X[i] = false;
    X[j - 1] = false;
    ans += 2 - (j == N);
    // debug(i, j, X, ans);
  }
  return ans;
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);

  int N, K;
  cin >> N >> K;
  string S;
  cin >> S;

  cout << solve(N, K, S) << '\n';

  return 0;
}