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.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scan = new Scanner(System.in);
    String str = scan.nextLine();
    String[] strs = str.split(" ");
    long x = Long.parseLong(strs[0]); // 今いる
    long k = Long.parseLong(strs[1]); // 回数
    long d = Long.parseLong(strs[2]); // 変動量

    if (x < 0) x = -x;

    long tmp = Math.floorDiv(x, d);
    if (k < tmp) {
      System.out.println(x - k * d);
      return;
    }
    long a = x - tmp * d;
    k -= tmp;
    System.out.println(Math.abs(a - d * (k % 2)));
  }
}