Problem:
Score : 300 points

Problem Statement

There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.

On this sequence, Snuke can perform the following operation:

Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.

Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times.
Find the minimum number of operations required.
It can be proved that, Under the constraints of this problem, this objective is always achievable.

Constraints

2 \leq K \leq N \leq 100000

A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N

Output

Print the minimum number of operations required.

Sample Input 1

4 3
2 3 1 4

Sample Output 1

2

One optimal strategy is as follows:

In the first operation, choose the first, second and third elements. The sequence A becomes 1, 1, 1, 4.

In the second operation, choose the second, third and fourth elements. The sequence A becomes 1, 1, 1, 1.

Sample Input 2

3 3
1 2 3

Sample Output 2

1

Sample Input 3

8 3
7 3 1 8 4 6 2 5

Sample Output 3

4

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

import           Control.Monad
import           Control.Monad.ST
import qualified Data.Array                  as A
import qualified Data.Array.ST               as ST
import qualified Data.Array.Unboxed          as AU
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Int
import qualified Data.IntMap                 as IM
import           Data.List
import qualified Data.Map                    as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                    as S
import           Data.Time
import qualified Data.Vector                 as V
import qualified Data.Vector.Mutable         as VM
import qualified Data.Vector.Unboxed         as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

readInt :: IO [Int]
readInt = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine

readInts :: Int -> IO [[Int]]
readInts n = replicateM n readInt

readString :: IO [String]
readString = map BS.unpack . BS.words <$> BS.getLine

readStrings :: Int -> IO [[String]]
readStrings n = replicateM n <$> readString

toPair :: [a] -> (a, a)
toPair [x, y] = (x, y)

main = do
  [n, k] <- readInt
  a <- readInt
  print $ solve n k a

solve n k a = b' + c'
  where
    b = takeWhile (/= 1) a
    c = tail $ dropWhile (/= 1) a
    b' = m (length b) (k - 1)
    c' = m (length c) (k - 1)

m a x
  | a `mod` x == 0 = a `div` x
  | otherwise = a `div` x + 1