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();
        x = Math.abs(x);
        long y = x / d;
        long pos = x % d;
        long neg = Math.abs(pos - d);
        if (y >= k) {
            System.out.println((y - k) * d + pos);
        } else {
            if ((k - y) % 2 == 0) {
                System.out.println(pos);    
            } else {
                System.out.println(neg);
            }
        }
	}
}