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 {
    private static final Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        final String[] XKD = sc.nextLine().split(" ");
        final Long X = Math.abs(Long.parseLong(XKD[0]));
        final Long K = Long.parseLong(XKD[1]);
        final Long D = Long.parseLong(XKD[2]);

        final Long M = X / D;
        final Long R = X % D;

        if (M > K) {
            System.out.println((M - K) * D + R);
        } else if ((K - M) % 2 == 0){
            System.out.println(R);
        } else {
            System.out.println(D - R);
        }
    }
}
