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 void main(String[] args) {
        try (Scanner sc = new Scanner(System.in)) {
            long X = sc.nextLong();
            long K = sc.nextLong();
            long D = sc.nextLong();

            X = Math.abs(X);

            if (K <= X / D) {
                System.out.println(Math.abs(X - D * K));
                return;
            }

            long l = 0;
            long r = K;
            for (; l + 1 < r;) {
                long c = (l + r) / 2;
                if (c <= X / D) {
                    l = c;
                } else {
                    r = c;
                }
            }

            if ((K - l) % 2 == 0) {
                System.out.println(Math.abs(X - l * D));
            } else {
                System.out.println(Math.abs(X - (l + 1) * D));
            }
        }
    }
}
