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 {
    public static void main(String[] args) {
        try (Scanner sc = new Scanner(System.in)) {
            long x = Long.parseLong(sc.next()); // axis
            long k = Long.parseLong(sc.next()); // count
            long d = Long.parseLong(sc.next()); // d

            // calc
            if (d <= Math.abs(x)) {
                long dnum = Math.min((Math.abs(x) / d), k);
                k = k - dnum;
                x = x - ((x >= 0) ? 1 : -1) * dnum * d;
            }
            if (k % 2 == 0) {
                System.out.println(Math.abs(x));
            } else {
                System.out.println(Math.abs(x + ((x > 0) ? -1 : 1) * d));
            }
        }
    }
}