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 scan = new Scanner(System.in);

		//入力値取得
		long X = scan.nextLong();
		long K = scan.nextLong();
		long D = scan.nextLong();

		//演算
		long result = 0L;

		if (Math.abs(X) / D >= K) {
			result = Math.min(Math.abs(X - K * D), Math.abs(X + K * D));
		} else if ((K - Math.abs(X) / D) % 2 == 0){
			result = Math.abs(X) % D;
		} else {
			result = D - Math.abs(X) % D;
		}

		//結果出力
			System.out.println(result);
	}
}
