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) throws Exception {
		Scanner sc = new Scanner(System.in);
		long x = sc.nextLong();
		long k = sc.nextLong();
		long d = sc.nextLong();
		sc.close();

		x = Math.abs(x);
		if (x / d >= k) {
			System.out.println(x - k * d);
		} else {
			long k2 = x / d;
			long x2 = x - k2 * d;
			long k3 = k - k2;
			k3 %= 2;
			x2 -= k3 * d;
			System.out.println(Math.abs(x2));
		}
	}
}
