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 stdIn = new Scanner(System.in);
		long X = Math.abs(stdIn.nextLong());
		long K = stdIn.nextLong();
		long D = stdIn.nextLong();
		
		//X = Math.abs(X);
		
		long ans = X;
		
		long step = Math.min(K, X / D);
		K -= step;
		X -= step * D;
		
		if(K % 2 == 0) {
//			System.out.println(X);
			ans = X;
		}else {
			ans = D - X;
//			System.out.println(D - X);
		}
		
		System.out.println(ans);
	}
}