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=sc.nextLong();
    long K=sc.nextLong();
    long D=sc.nextLong();
    long div=0;
    long num=0;
    long ndiv=0;
    if(X>0){
    div=(long)Math.ceil
    ((double)X/(double)D);
    ndiv=Math.min(div,K);
    num=X-D*ndiv;
    }
    else if(X<0)
    {
      div=(long)Math.ceil
    ((double)Math.abs(X)/(double)D);
    ndiv=Math.min(div,K);
    num=X+D*ndiv;
    }
    K-=ndiv;
    long ans=0;
    if(K%2==0)
    {
      ans=Math.abs(num);
    }
    else
    {
      if(num<0)
      ans=Math.abs(num+D);
      else
      ans=Math.abs(num-D);
    }
    System.out.println(ans);
  }
}
    