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.*;

class Main{
    static Scanner sc = new Scanner(System.in);
    public static void main(String args[]){
        long X=Math.abs(sc.nextLong()),K=sc.nextLong(),D=sc.nextLong(),end=0,endl=0;
        if(K>X/D){
            if(X-(X/D)*D<((X/D)+1)*D-X){
                end=X-(X/D)*D;
                endl=D-end;
                if((K-X/D)%2==0){
                    System.out.println(end);
                }else{
                    System.out.println(endl);
                }
            }else{
                endl=X-(X/D)*D;
                end=D-endl;
                if((K-(X/D)-1)%2==0){
                    System.out.println(end);
                }else{
                    System.out.println(endl);
                }
            }
        }
        else{
            System.out.println(Math.abs(X-D*K)<Math.abs(X+D*K)?Math.abs(X-D*K):Math.abs(X+D*K));
        }
    }
}