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.Scanner;
import static java.lang.System.*;
import static java.lang.Math.*;

public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(in);
    long x,k,d;
    x = abs(sc.nextLong());
    k = sc.nextLong();
    d = sc.nextLong();
    
    long devide = x/d;
    
    if(devide >= k){ //pvOverFlow
      out.println(x - k*d);
      
    }else if((k - devide) %2 == 0){
      out.println(x % d);
      
    }else{
      out.println(d - x%d);
    }
    sc.close();
  }
}