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 Scala (2.13.1) (judge verdict: Accepted)

import scala.io.StdIn._

object Main extends App {

  val Array(x,k,d) = readLine().split(" ").map(_.toLong)

  def solve() = {
    val xAbs = x.abs
    val movedCnt = xAbs / d
    if(k > movedCnt) {
      val nearP = xAbs % d
      val farP = (xAbs - d).abs
      val fixP = Math.min(nearP, farP)

      if(fixP == nearP) {
        val restMoveCnt = k - movedCnt
        if(restMoveCnt % 2 == 0) nearP else (nearP - d).abs
      } else {
        val restMoveCnt = k - movedCnt - 1
        if(restMoveCnt % 2 == 0) farP else (farP - d).abs
      }
    } else {
      xAbs - (k * d)
    }
  }

  println(solve())

}