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.

Examples

Input

6 2 4


Output

2


Input

7 4 3


Output

1


Input

10 1 2


Output

8


Input

1000000000000000 1000000000000000 1000000000000000


Output

1000000000000000
import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    long x = sc.nextLong();
    long k = sc.nextLong();
    long d = sc.nextLong();
    long ans = 0;
    if(x >= 0) {
      long t = (x + d - 1) / d;
      if(t <= k) {
        if((t % 2) == (k % 2)) {
          ans = Math.abs(x - (t * d));
        } else {
          ans = x - (t * d) + d;
        }
      } else {
        ans = x - (k * d);
      }
    } else {
      long t = (d - x - 1) / d;
      if(t <= k) {
        if((t % 2) == (k % 2)) {
          ans = Math.abs(x + (t * d));
        } else {
          ans = Math.abs(x + (t * d) - d);
        }
      } else {
        ans = Math.abs(x + (k * d));
      }
    }
    System.out.println(ans);
  }
}