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 = (long)Math.abs(sc.nextLong());
		long k = sc.nextLong();
		long d = sc.nextLong();

		if ( x<=d ) {
			if ( k%2==0 ) System.out.println(x);
			else          System.out.println(d-x);
			System.exit(0);
		}

		long t = x/d ;
		if ( t>=k ) {
			System.out.println(x - d*k);
			System.exit(0);
		}

		long xt = x - d*t ;
		if ( (k-t)%2==0 ) System.out.println(xt);
		else              System.out.println(d-xt);
	}
}