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();
	if (x < 0) x = -x;
	if (x/d >= k) {
	    System.out.print(x - k*d);
	} else {
	    k = k - x/d;
	    x = x - x/d * d;
	    if (k%2 == 1) System.out.print(Math.abs(x - d));
	    else { System.out.print(x); }
	}
    }
}
