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 final int MOD = 1000000007;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long x = Long.parseLong(sc.next());
        long k = Long.parseLong(sc.next());
        long d = Long.parseLong(sc.next());
        if (x > 0 && (x * 1.0 / k >= d)) {
            System.out.println(x - k * d);
            return;
        } else if (x < 0 && (x * (-1.0)) / k >= d) {
            System.out.println(Math.abs(x + k * d));
            return;
        }
        if (x > 0) {
            long num = (long)Math.ceil(x * 1.0 / d);
            long xx = x - ((num - 1) * d);
            if ((k - (num - 1)) % 2 == 0) {
                System.out.println(xx);
            } else {
                System.out.println(Math.abs(xx - d));
            }
        } else if (x < 0) {
            long num = (long)Math.ceil(x * (-1.0) / d);
            long xx = x + ((num - 1) * d);
            if ((k - (num - 1)) % 2 == 0) {
                System.out.println(Math.abs(xx));
            } else {
                System.out.println(Math.abs(xx + d));
            }
        } else {
            if (k % 2 == 0) {
                System.out.println(0);
            } else {
                System.out.println(d);
            }
        }
    }
}