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) {
		Scanner sc = new Scanner(System.in);
		long x = sc.nextLong();
		long k = sc.nextLong();
		long d = sc.nextLong();
		long ax = Math.abs(x);
		if(ax/d > k) {
			System.out.println(ax-k*d);
		}
		else {
			k -= ax/d;
			ax = ax - d*(ax/d);
			if(k%2==0) {
				System.out.println(ax);
			}
			else {
				System.out.println(Math.abs(ax-d));
			}
		}
	}
}