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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public final class Main {

    public static void main(String[] args) {
        final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        final String[] line = in.nextLine().split(" ");
        long x = Long.parseLong(line[0]);
        long k = Long.parseLong(line[1]);
        long d = Long.parseLong(line[2]);
        x = Math.abs(x);
        if ((x / d) >= k) {
            System.out.println(x - d * k);
        } else {
            k -= x / d;
            long r = x % d;
            if (k % 2 == 0) {
                System.out.println(r);
            } else {
                System.out.println(d - r);
            }
        }
    }
}
