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.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long X = Long.parseLong(scanner.next());
        long K = Long.parseLong(scanner.next());
        long D = Long.parseLong(scanner.next());
        long div = 0;
        long left = 0;
        long right = 0;
        scanner.close();

        X = Math.abs(X);
        div = X / D;

        if (div > K){
            X -= K * D; 
        } else {
            X -= div * D;
            left = D - X;
            right = X;

            if ((K - div) % 2 == 0){
                X = right;
            } else {
                X = left;
            }
        }
        
        System.out.println(Math.abs(X));
    }
}


