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.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner scan = new Scanner(System.in);
        long X = scan.nextLong();
        X = Math.abs(X);
        long K = scan.nextLong();
        long D = scan.nextLong();
        
        if(K <= X/D){
            System.out.println(Math.abs(X-D*K));
            return;
        }
        
        K -= X/D;
        X %= D;
        
        if(K%2==0) System.out.println(Math.abs(X));
        else System.out.println(Math.abs(X-D));
    }
}