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.lang.*;
import java.io.*;

public class Main
{
    public static void main (String[] args)
    {
        // your code goes here
        Scanner s = new Scanner(System.in);
        long x = Math.abs(s.nextLong());
        long k = s.nextLong();
        long d = s.nextLong();
        long q = x/d;
        long r =  (x%d);
        long r1 =  (d-r);
//        System.out.println(q);
//        System.out.println(r+" "+r1);
        long m;
        if(q>=k)
            m = x-k*d;
        else
        {
            k-=q;
            if(k%2==1)
                m=r1;
            else
                m=r;
        }
        System.out.println(m);
    }
}