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 static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long x = sc.nextLong(), k = sc.nextLong(), d = sc.nextLong();
        x = Math.abs(x);
        if(x/d >= k){
            System.out.println(x-k*d);
        }else{
            long newX = x % d;
            long newK = k - x / d;
            if(newK % 2 == 0){
                System.out.println(Math.min(newX, 2 * d - newX));
            }else{
                System.out.println(Math.min(newX + d, d - newX));
            }
        }
    }
}
