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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T

main :: IO ()
main = do
  (n : k : _) <- map unsafeSignedDecimal . T.words <$> T.getLine :: IO [Int]
  ds <- map (== 'R') <$> getLine :: IO [Bool]
  let
    d1 = head ds
    (h, x, o, Just dn) = foldl step (0, 0, 0, Nothing) $ ds :: (Int, Int, Int, Maybe Bool)
    step (h, x, o, Just d') d | d' && not d = (h, succ x, o, Just d)
                              | not d' && d = (h, x, succ o, Just d)
                              | otherwise = (succ h, x, o, Just d)
    step _ d = (0, 0, 0, Just d)
    m = min x o
  print $ h + f k m (x - m) (o - m) d1 dn

f :: Int -> Int -> Int -> Int -> Bool -> Bool -> Int
f k m x o d1 dn
  | k <= m = 2 * k
  | otherwise
    =
      let
          k' = k - m
          a = if not d1 && 1 <= o then 1 else 0
          b = if dn && 1 <= x then 1 else 0
        in
          2 * m + min k' (a + b)

unsafeSignedDecimal :: T.Text -> Int
unsafeSignedDecimal s = case T.signed T.decimal s of
  Right (n, _) -> n