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 = Long.parseLong(sc.next());
    long k = Long.parseLong(sc.next());
    long d = Long.parseLong(sc.next());
    
    long ans = x;
    long divAns = x/d;

    if(k < Math.abs(divAns)){
      if(x > 0){
        ans = x - d * k;
      }else{
        ans = x + d * k;
      }
      
      System.out.println(Math.abs(ans));
      sc.close();
      return;
    }

    k = k - Math.abs(divAns);
    ans = x - d * divAns;

    if(k % 2 != 0){
      if(ans > 0){
        ans = ans - d;
      }else{
        ans = ans + d;
      }
    }

    System.out.println(Math.abs(ans));
   
    sc.close();
    return;
  }
  
}
