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 scan = new Scanner(System.in)){
			long X = scan.nextLong();
			long K = scan.nextLong();
			long D = scan.nextLong();



		long absX = Math.abs(X);
		long ans;
		if(absX/D<K) {//あまりにたどり着くまでの回数よりKが大きいなら
			long k = K-absX/D;
			ans = k%2==0?absX%D:D-absX%D;
			System.out.println(ans);
		}else {
			 ans = absX-D*K;
			System.out.println(ans);
		}


		}
	}


}
