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.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.function.*;
import java.util.regex.*;
import java.util.stream.*;
import static java.util.stream.Collectors.joining;
import static java.util.stream.Collectors.toList;
 
public class Main
{
    public static void main(String[] args)
    {
        Scanner in=new Scanner(System.in);
        long x=in.nextLong();
        long k=in.nextLong();
        long d=in.nextLong();
        if(x<0)
        {
            long y=Math.abs(x)/d;
            long x1=x+y*d;
            if(y>=k)
                System.out.println(Math.abs(x+k*d));
            else
            {
                if(((k-y)&1)==0)
                    System.out.println(Math.abs(x1));
                else
                    System.out.println(x1+d);
            }
        }
        else if(x>0)
        {
            long y=x/d;
            long x1=x-y*d;
            if(y>=k)
                System.out.println(x-k*d);
            else
            {
                if(((k-y)&1)==0)
                    System.out.println(x1);
                else
                    System.out.println(Math.abs(x1-d));
            }
        }
        else
        {
            if((k&1)==0)
                System.out.println(0);
            else
                System.out.println(d);
        }
    }
}
