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 scan = new Scanner(System.in);
		long x = scan.nextLong();
		long k = scan.nextLong();
		long d = scan.nextLong();
		x = Math.abs(x);

			if(x/d > k){
				System.out.print(x-d*k);
				return;
			}else{
				k -= x/d;
				x -= d*(x/d);
				if(k%2 == 0){
					System.out.print(x);
				}else{
					System.out.print(Math.min(Math.abs(x+d),(Math.abs(x-d))));
				}

		}
	}
}
