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.*;

public class Main {

    Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        new Main().run();
    }

    void run() {

        long x = sc.nextLong();
        long k = sc.nextLong();
        long d = sc.nextLong();

        long absX = Math.abs(x);

        long tmpMove = absX / d;
        long tmpMulti = k * d;

        if (k <= tmpMove) {
            if (0 < x) System.out.println(x - tmpMulti);
            else System.out.println(Math.abs(x + tmpMulti));
        } else {
            if (0 < x) {
                x -= d * tmpMove;
                long res = Math.abs(x);
                k -= tmpMove;
                if (k % 2 == 0) {
                    System.out.println(res);
                } else {
                    System.out.println(Math.min(Math.abs(x - d), Math.abs(x + d)));
                }
            } else {
                x += d * tmpMove;
                long res = Math.abs(x);
                k -= tmpMove;
                if (k % 2 == 0) {
                    System.out.println(res);
                } else {
                    System.out.println(Math.min(Math.abs(x - d), Math.abs(x + d)));
                }
            }
        }


    }


}

