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 sc = new Scanner(System.in);
    long x = sc.nextLong();
    long k = sc.nextLong();
    long d = sc.nextLong();

    System.out.println(solve(Math.abs(x), k, d));
  }
  static long solve(long x, long k, long d){
    long a = x / d;
    if(a == 0){
      if(k % 2 == 0){
        return x;
      } else {
        return Math.abs(x - d);
      }
    } else if(a >= k){
      x = x - (k * d);
      return Math.abs(x);
    } else {
      // (a < k)
      x = x - (a * d);
      k -= a;
      if(k % 2 == 0){
        return Math.abs(x);
      } else {
        return Math.abs(Math.abs(x) - d);
      }
    }
  }
}