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 {
	long X;
	long K;
	long D;
	long ans = Long.MAX_VALUE;

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		Main main = new Main();
		main.main(scan);
	}

	public void main(Scanner scan) {
		X = Long.parseLong(scan.next());
		K = Long.parseLong(scan.next());
		D = Long.parseLong(scan.next());
		scan.close();
		System.out.println(Walking());
	}

	public long Walking() {
		X = Math.abs(X);
		long k = Math.min(K,X/D);
		K -= k;
		X -= k*D;

		if (K % 2 == 0) {
			ans = X;
		} else {
			ans = Math.abs(X - D);
		}
		return ans;
	}

}
