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 qualified Data.Vector.Unboxed as V
import Data.Array.IArray (listArray, accumArray, (!))
import Data.Array.MArray
import Data.Array.ST (STUArray, runSTUArray)
import Data.Array.Unboxed (UArray)
import Data.List (sortOn, sortBy, unfoldr, partition)
import Data.Char (isSpace)
import Control.Monad.ST (ST)
import Control.Monad.Trans.State (StateT(..))
import Control.Arrow ((***), second)
import qualified Data.ByteString.Char8 as B

-- utility functions

--   Input functions
readInt = B.readInt . B.dropWhile isSpace

readInts :: Int -> B.ByteString -> [Int]
readInts n = take n . unfoldr readInt

readIntsV :: Int -> B.ByteString -> V.Vector Int
readIntsV n = V.unfoldrN n readInt

readIntsA :: Int -> B.ByteString -> UArray Int Int
readIntsA n bs = runSTUArray $ do
  arr <- newArray_ (0,n-1)
  go arr 0 bs
  return arr
  where
    go :: STUArray s Int Int -> Int -> B.ByteString -> ST s ()
    go arr i bs
      | i==n = return ()
      | otherwise = do
        let Just (x,bs') = readInt bs
        writeArray arr i x
        go arr (i+1) bs'

readTsV :: Int -> B.ByteString -> V.Vector (Int,Int)
readTsV n = V.unfoldrN n $ runStateT ((,) <$> StateT readInt <*> StateT readInt)

readTs :: Int -> B.ByteString -> [(Int,Int)]
readTs n = take n . unfoldr readT where
  readT = runStateT ((,) <$> StateT readInt <*> StateT readInt)

-- main

solv k as = div (lbfr1+k-2) (k-1) + div (laft1+k-2) (k-1) where
  (lbfr1, laft1) = second (subtract 1) $ V.length *** V.length $ V.break (==1) as

main = do
  [n,k] <- map read . words <$> getLine
  as <- readIntsV n <$> B.getLine
  print $ solv k as