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 long getDestination(long x, long k, long d) {
        long prevValue = 0;
        long prevPrevValue = 0;
        while (k > 0) {
            if (x == 0) {
                if (k % 2 == 0) {
                    return 0;
                } else {
                    return d;
                }
            } else {
                long jumpK = Math.abs(x) / d;
                jumpK = Math.max(jumpK, 1);
                jumpK = Math.min(jumpK, k);

                k -= jumpK;
                if (x > 0) {
                    x -= jumpK * d;
                } else {
                    x += jumpK * d;
                }

                if (prevPrevValue == x) {
                    if (k % 2 == 0) return Math.abs(x);
                    if (x > 0) return Math.abs(x - d);
                    if (x < 0) return Math.abs(x + d);
                }
                prevPrevValue = prevValue;
                prevValue = x;
            }
        }

        return Math.abs(x);
    }

    public static void main(String[] args) throws Exception {
        Main solution = new Main();

        Scanner scanner = new Scanner(System.in);
        long x = scanner.nextLong();
        long k = scanner.nextLong();
        long d = scanner.nextLong();

        long answer = solution.getDestination(x, k, d);
        System.out.println(answer);
    }
}