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{
public static void main(String[]args){
  Scanner sc=new Scanner(System.in);
  long x=Math.abs(sc.nextLong());
  long k=sc.nextLong();
  long d=sc.nextLong();
  if(k-x/d<=0){
    System.out.println(x-k*d);
  }else{
  k-=x/d;
  System.out.println(k%2==0?x-d*(x/d):Math.abs(x-d*(x/d)-d));}
}
}
