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
//I AM THE CREED
/* //I AM THE CREED
/* package codechef; // don't place package name! */
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.util.*;
import java.awt.Point;
public class Main{
    public static void main(String[] args) throws IOException 
    { 
  
        Scanner input = new Scanner(System.in);
        while(input.hasNext()){
            long x=input.nextLong();
            long k=input.nextLong();
            long d=input.nextLong();
            x=Math.abs(x);
            if(k<=x/d){
                System.out.println(x-k*d);
                continue;
            }
            long min=Long.MAX_VALUE;
            if((k-(x/d))%2==0){
                min=x%d;
            }
            else{
                min=d-(x%d);
            }
            System.out.println(min);
        }
        
    }
    


}