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);
        // 整数の入力
        long X=Math.abs(sc.nextLong());
        long K=Math.abs(sc.nextLong());
        long D=Math.abs(sc.nextLong());
        long result=0;
        if(X/D-K>0){
            result=X-K*D;
        }else{
            if(K%2==1){
                X=Math.abs(X-D);
                K=K-1;
            }
            long K2=((long)(X/D/2))*2;
            result=Math.min(X-K2*D,Math.abs(X-(K2+2)*D));
        }


        System.out.println(result);

    }
}