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);
        long x = Long.parseLong(scan.next());
        long k = Long.parseLong(scan.next());
        long d = Long.parseLong(scan.next());
        scan.close();

        long ans = 0;
        long absX = Math.abs(x);
        if (absX / d >= k) {
            ans = absX - k * d;
        } else {
            long sho = absX / d;
            long amari = absX % d;
            if ((k - sho) % 2 == 0) {
                ans = amari;
            } else {
                ans = d - amari;
            }
        }

        System.out.println(ans);
    }
}
