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.*;
 
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long x = Long.parseLong(sc.next());
        long k = Long.parseLong(sc.next());
        long d = Long.parseLong(sc.next());
        long ans = 0;
        if(x < 0) {
            x = -x;
        }
        ans = x % d;
        if((k - x/d) < 0) {
            ans = x - d*k;
        }else if((k - x / d) % 2 == 1) {
            ans -= d;
        }
        
        if(ans < 0) ans = -ans;  
        System.out.println(ans);  
    }
}