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;

/**
 * Created by enpingkuang on 2020/9/20 11:36 下午
 */
public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long x = scanner.nextLong();
        long k = scanner.nextLong();
        long d = scanner.nextLong();
        x = Math.abs(x);
        long n = x/d;
        if(x%d !=0)n++;
        if(n > k){
            System.out.println(x-k*d);
        }else{
            long tmp = k - n;
            if(tmp % 2 == 1){
                System.out.println(x - (n-1)*d);
            }else{
                System.out.println(Math.abs(x-n*d));
            }
        }
    }
}
