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: Wrong Answer)


import scala.io.StdIn

object Main extends App {
  val Array(x,k,d):Array[Long] = StdIn.readLine().split(' ').map(_.toLong)
  val stepToZeroNbhd = x / d
  val ans =
    if(stepToZeroNbhd >= k)
      x - math.signum(x)*d*k
    else{
      val x2=x - math.signum(x)*d*stepToZeroNbhd
      val kRemaining=k-stepToZeroNbhd
      if(kRemaining % 2 == 0 )
        x2
      else {
        val sgn = if(x2==0) 1 else math.signum(x2)
        x2 - sgn*d
      }
    }

  println(math.abs(ans))

}