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.*;
import java.lang.*;
class Main{
    public static void main(String args[]) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        long x = Long.parseLong(st.nextToken());
        long k = Long.parseLong(st.nextToken());
        long d = Long.parseLong(st.nextToken());

        long mov = Math.abs(x/d);

        if(mov >= k){
            if(x<0){
               System.out.println(Math.abs(x+k*d)); 
            }
            else{
                System.out.println(Math.abs(x-k*d));
            }
        }
        else if(mov < k){
            long num = k-mov;
            if(x<0){
                
                x = x+mov*d;
                if(num%2==1){
                    long dist  = Math.min(Math.abs(x-d),Math.abs(x+d));
                    System.out.println(dist);
                }
                else{
                    System.out.println(Math.abs(x));
                }

            }
            else{
                x = x-mov*d;
                //x = x+mov*d;
                if(num%2==1){
                    long dist  = Math.min(Math.abs(x-d),Math.abs(x+d));
                    System.out.println(dist);
                }
                else{
                    System.out.println(Math.abs(x));
                }
            }
        }
    }
}