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;
public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    long X = sc.nextLong();
    X=Math.abs(X);
    long K = sc.nextLong();
    long D = sc.nextLong();
    long quo = X/D; //商; 0 に到達するまでの回数
    long ans = 0;
    
    if(quo>=K) {
      ans=X-K*D;
    } else {
      if((K-quo)%2 == 0) {
        ans=X-quo*D;
      } else {
        ans=X-(quo+1)*D;
      }
    }
    
    System.out.println(Math.abs(ans));
  }
}