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.PrintWriter;
import java.util.*;

public class Main {
    void run() {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        long x = sc.nextLong();
        long k = sc.nextLong();
        long d = sc.nextLong();

        if (x == 0) {
            System.out.println(k % 2 == 0 ? 0 : d);
            return;
        }

        long maxCount = Math.abs(x / d);
        long absD = x < 0 ? -d : d;
        if (maxCount >= k) {
            debug(1);
            System.out.println(Math.abs(x - k * absD));
        } else {
            long nokori = k - maxCount;
            if (nokori % 2 == 0) {
                debug(3);
                System.out.println(Math.abs(x % d));
            } else {
                debug(4);
                System.out.println(Math.abs(x % d - absD));
            }
        }
        // out.println("Hello World");
        out.flush();
    }

    void debug(Object... os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}
