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.*;
import java.io.*;
public class Main extends PrintWriter {
    Main()
    {
        super(System.out);
    }
    public static void main(String args[]) {
      Main o=new Main();
      o.main();
      o.flush();
      o.close();
    }
    void main()
    {
        Scanner sc=new Scanner(System.in);
        long x=sc.nextLong();
        long k=sc.nextLong();
        long d=sc.nextLong();
        long rem=x%d;
        long quo=x/d;
        if(x<0)
        quo*=-1;
        if(k<quo)
        {
            if(x>0)
            {
                println(Math.abs(x-(k*d)));
            }
            else
            {
                println(Math.abs(x+(k*d)));
            }
        }
        else
        {
            if(x>=0)
            {
                long v1=rem-d;
                long rem1=k-quo;
                if(rem1%2==0)
                println(Math.abs(rem));
                else
                println(Math.abs(v1));
            }
            else
            {
                long v2=rem+d;
                long rem2=k-quo;
                if(rem2%2==0)
                println(Math.abs(rem));
                else
                println(Math.abs(v2));
            }
        }
        sc.close();
    }
}