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.*;

public class Main {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        long x = scan.nextLong();
        long k = scan.nextLong();
        long d = scan.nextLong();
        long num = Math.abs(x) / d;
        if (k <= num) {
            if (x > 0) x -= k * d;
            else x += k * d;
            System.out.println(Math.abs(x));
            return;
        }
        x = x % d;
        k -= num;
        if (x > 0 && k > 0) {
            x -= d;
            k--;
        }
        long tmp = k % 2 == 1 ? x + d : x;
        long ans = Math.abs(tmp);
        System.out.println(ans);
    }
}
