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){
		try(Scanner sc = new Scanner(System.in)) {
			
			long x = sc.nextLong();
			long k = sc.nextLong();
			long d = sc.nextLong();
			
			
			long ans = 0;
			long step = Math.abs(x) / d;
			x = Math.abs(x);

			if ( k <= step ) {
				ans = x - k * d;
			}
			else {
				long additionalStep = k - step;
				if ( additionalStep % 2 == 0 ) {
					//can go minimum
					ans = x % d;
				}
				else {
					//should go opposite side
					ans = d - x % d;
				}
				
			}
			
			System.out.println(ans);
		}
	}

}