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.*;

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();
		sc.close();

		long c = Math.abs(X) / D;

		long ans = Long.MAX_VALUE / 2;
		// 収束しない場合
		if (K < c) {
			ans = Math.abs(X) - D * K;
		} else {
			// 収束する場合
			long std = Math.abs(X) - D * c;
			long rest = K - c;
			if (rest % 2 == 0) {
				ans = std;
			} else {
				if (std >= 0) {
					ans = std - D;
				} else {
					ans = std + D;
				}
			}
		}
		System.out.println(Math.abs(ans));
	}
}
