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 Python (3.4.3) (judge verdict: Accepted)

n, k = map(int, input().split())
s = [x for x in input()]

start = s[0]
current = 1
prev = None
utility = 0
while k != 0 and current < n:
  if s[current] != start:
    if not prev:
      prev = current
    else:
      utility += 1
  elif prev:
    if current == n:
      utility += 1
    else:
      utility += 2
    k = k-1
    prev = None
  else:
    utility += 1
  current += 1

if prev:
  if current == n and k > 0:
    utility +=  1
  if start == 'L':
    prev = 'R'
  else:
    prev = 'L'
else:
  if start == 'R':
    prev = 'R'
  else:
    prev = 'L'
while current < n:
  if s[current] == prev:
    utility += 1
  prev = s[current]
  current += 1
print(utility)