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;
import java.util.Stack;

public class Main {
  static int[][] numbers;
  public static void main(String[] args) {
    // TODO Auto-generated method stub
    Scanner in = new Scanner(System.in);
    long x= in.nextLong();
    long k = in.nextLong();
    long d = in.nextLong();

    x = Math.abs(x);
    if(x>0 && (x/d)>=k) {
       long q = x/d;
       x = x-(k)*d;

    } else {
      long y = x/d;
      x =x -(y)*d;
      k -=y;
      if(k%2==0)
        x= Math.abs(x);
      else
        x = Math.min(Math.abs(x-d),Math.abs(x+d));
    }

    System.out.println(x);     
  }
  
  
}
