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 min1 = x % d;
		if(min1 < 0)
			min1 += d;
		long min2 = min1 - d;
		long ans = Long.MAX_VALUE / 2;
		long sa1 = Math.abs(x - min1) / d % 2;
		if(sa1 < 0)
			sa1 += 2;
		long sa2 = Math.abs(x - min2) / d % 2;
		if(sa2 < 0)
			sa2 += 2;
		if(Math.abs(x - min1) / d <= k && sa1 == k % 2) {
			ans = Math.abs(min1);
		}
		if(Math.abs(x - min2) / d <= k && sa2 == k % 2) {
			ans = Math.abs(min2);
		}
		long ans2 = 0;
		if(x >= 0) {
			ans2 = Math.abs(x - k * d);
		}
		else {
			ans2 = Math.abs(x + k * d);
		}

		ans = Math.min(ans, ans2);


		sc.close();
		System.out.println(ans);

	}
}

