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 {

	static long solve(long x, long k, long d) {
		x = Math.abs(x);
		long q = x / d;
		long r = x % d;
		if (q >= k)
			return x - d * k;
		long remaining = k - q;
		if (remaining % 2 == 0)
			return r;
		else
			return d - x % d;
	}

	public static void main(String[] args) {
		Scanner stdIn = new Scanner(System.in);
		long x, k, d;

		x = stdIn.nextLong();
		k = stdIn.nextLong();
		d = stdIn.nextLong();
		System.out.println(solve(x, k, d));

		stdIn.close();
	}
}
