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 static java.lang.Math.*;

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

class Main{
    static void walkingTakashi(List<Long> list, long X, long K, long D) {
        long x = abs(X);
        if (x / D >= K)
            list.add(x - D * K);
        else {
            //(x / D)回移動するので, (x / D)*Dだけxは進む
            long k = K - x / D;
            x -= (x / D) * D;
            //往復
            if (k % 2 == 0)
                list.add(x);
            else
                list.add(abs(x - D));
        }

    }

    public static void main(String[] args) {
        Scanner std = new Scanner(System.in);
        long X = std.nextLong();
        long K = std.nextLong();
        long D = std.nextLong();

        List<Long> list = new ArrayList<Long>();
        walkingTakashi(list, X, K, D);

        Collections.sort(list);
        System.out.println(list.get(0));
    }

}
