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.security.SecureRandom;
import java.sql.Array;
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();
        x=Math.abs(x);
        if (x/d>=k) System.out.println((x-k*d));
        else{
            k-=x/d;
            x-=(x/d)*d;
            if (k%2==0){
                System.out.println(x);
            }
            else{
                System.out.println(Math.abs((x-d)));
            }
        }
    }

}

