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: Accepted)

import Data.List
import Data.Char
import Data.Maybe
import Control.Monad
import qualified Data.ByteString.Char8 as BS8
import qualified Data.Vector as Vector
import Data.Vector ((!))

main :: IO ()
main = do
  [x, k, d] <- unfoldr (BS8.readInteger . BS8.dropWhile isSpace) <$> BS8.getLine

  let
    (n, m) = (abs x) `divMod` d
    o = minimum $ map abs [m - d, m + d]
    ans = abs $ if k >= n then
        if (k - n) `mod` 2 == 0 then m else o
      else minimum $ map abs [x + k * d, x - k * d]

  print ans