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){

		Scanner sc = new Scanner(System.in);
		Long X = sc.nextLong();
		Long K = sc.nextLong();
		Long D = sc.nextLong();

		if(X < 0){
			X *= -1;
		}

		Long cnt = (long) Math.floor(X/D);

		if(cnt == 0){
			if(K%2==0){
				System.out.println(X);
				return;
			}else{
				System.out.println(Math.abs(X-D));
				return;
			}
		}

		if(K < cnt){
			System.out.println(X-D*K);
			return;
		}
		  
		if((K-cnt)%2==0){
			System.out.println(X-D*cnt);
			return;
		}else{
			System.out.println(Math.abs(X-D*(cnt+1)));
			return;
		}

	}
}
