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);
               long x=scan.nextLong();
               long k=scan.nextLong();
               long d=scan.nextLong();
               x=Math.abs(x);
               if(x>0 && (x/d)>=k){
                   long qq=x/d;
                   x=x-k*d;
                   System.out.print(x);
                   return;
               }
               long y=x/d;
               x=x-y*d;
               k=k-y;
               if(k%2==0){
                   System.out.print(Math.abs(x));
               }else{
                   System.out.print(Math.min(Math.abs(x-d),Math.abs(x+d)));
               }
    }
}
