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) {
		// TODO Auto-generated method stub
        Scanner sc=new Scanner(System.in);
        long x=sc.nextLong();
        long k=sc.nextLong();
        long d=sc.nextLong();
        
        x=Math.abs(x);
        long q=k-(x/d);
        long p=x%d;
        if(q<0)
        {
        	System.out.println((x-(k*d)));
        	System.exit(0);
        }
        else
        {
        	if(q%2==1)
        		System.out.println(Math.min(Math.abs(p-d),Math.abs(p+d)));
        	else
        		System.out.println(p);
        }
        
	}

}
