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 {
	//java11

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		long X = sc.nextLong();
		long K = sc.nextLong();
		long D = sc.nextLong();

		if(X < 0) {
			X = -X;
		}

		long min_plus_n = X / D;
		long min_plus = X % D;
		long min_minus_n = min_plus_n + 1;
		long min_minus = Math.abs(min_plus-D);

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

		if(K % 2 == min_plus_n % 2) {
			System.out.println(min_plus);
		}else {
			System.out.println(min_minus);
		}

	}


}
