Problem:
Score : 300 points

Problem Statement

Takahashi, who lives on the number line, is now at coordinate X. He will make exactly K moves of distance D in the positive or negative direction.

More specifically, in one move, he can go from coordinate x to x + D or x - D.

He wants to make K moves so that the absolute value of the coordinate of the destination will be the smallest possible.

Find the minimum possible absolute value of the coordinate of the destination.

Constraints

-10^{15} \leq X \leq 10^{15}

1 \leq K \leq 10^{15}

1 \leq D \leq 10^{15}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X K D

Output

Print the minimum possible absolute value of the coordinate of the destination.

Sample Input 1

6 2 4

Sample Output 1

2

Takahashi is now at coordinate 6. It is optimal to make the following moves:

Move from coordinate 6 to (6 - 4 =) 2.

Move from coordinate 2 to (2 - 4 =) -2.

Here, the absolute value of the coordinate of the destination is 2, and we cannot make it smaller.

Sample Input 2

7 4 3

Sample Output 2

1

Takahashi is now at coordinate 7. It is optimal to make, for example, the following moves:

Move from coordinate 7 to 4.

Move from coordinate 4 to 7.

Move from coordinate 7 to 4.

Move from coordinate 4 to 1.

Here, the absolute value of the coordinate of the destination is 1, and we cannot make it smaller.

Sample Input 3

10 1 2

Sample Output 3

8

Sample Input 4

1000000000000000 1000000000000000 1000000000000000

Sample Output 4

1000000000000000

The answer can be enormous.

Solution in Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

import Control.Monad
import Data.Function
import Data.Char
import Data.List
import Text.Read
import Text.ParserCombinators.ReadPrec
import Text.Printf

import Data.Ratio
import Data.Maybe

newtype Pair a b = Pair { getPair :: (a, b) }

instance (Read a, Read b) => Read (Pair a b) where
  readPrec = Pair `dot` (,) <$> readPrec <* get <*> readPrec

instance (Show a, Show b) => Show (Pair a b) where
  show (Pair (a, b)) = show a ++ " " ++ show b

readPair :: IO (Int, Int)
readPair = getPair <$> readLn

infixr 8 `dot`
dot :: (c -> d) -> (a -> b -> c) -> a -> b -> d
dot = ((.).(.))

main :: IO ()
main = do
  [x, k, d] <- map read . words <$> getLine
  case solve x k d of
    Just ans -> print ans
    _        -> return ()

solve :: Int -> Int -> Int -> Maybe Int
solve x k d
  | k < 0  = Nothing
  | d <= 0 = Nothing
  | k == 0 = Just $ abs x
  | x > 0  = solve (x - d) (k - 1) d
  | x <= 0 = solve (x + d) (k - 1) d