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();
    if(X<0){X=-X;}
    long K =sc.nextLong();
    long D =sc.nextLong();
    long w =X/D;
    long ans;
    if(w>K){ans=X-K*D;}
    else{
      long z = X-w*D;
      long p =K-w;
      if(p%2==0){ans =z;}
      else{ans =z-D;}
    }
    ans =Math.abs(ans);
    System.out.println(ans);
  }
}