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 sc = new Scanner(System.in);
		long X = sc.nextLong();
        long K = sc.nextLong();
        long D = sc.nextLong();
        long res;
        long tika = Math.abs(X)/D;
        if(K<=tika){
            res = Math.abs(X) - D*K;
        }else if((K-tika)%2==0){
            res = Math.abs(X) - D*tika;
        }else{
            res = D*(tika+1) - Math.abs(X);
        }
		System.out.println(res);
	}
}