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
//Created by Aminul on 8/15/2020.

import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        long x = in.nextLong(), k = in.nextLong(), d = in.nextLong();
        long div = abs(x) / d;
        div = min(div, k);
        k -= div;
        if (k % 2 == 1) {
            div++;
        }

        if (x < 0) pw.println(abs(x + (div * d)));
        else pw.println(abs(x - (div * d)));
        pw.close();
    }

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