Problem: There is a polyline going through points (0, 0) – (x, x) – (2x, 0) – (3x, x) – (4x, 0) – ... - (2kx, 0) – (2kx + x, x) – .... 

We know that the polyline passes through the point (a, b). Find minimum positive value x such that it is true or determine that there is no such x.

Input

Only one line containing two positive integers a and b (1 ≤ a, b ≤ 109).

Output

Output the only line containing the answer. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 9. If there is no such x then output  - 1 as the answer.

Examples

Input

3 1


Output

1.000000000000


Input

1 3


Output

-1


Input

4 1


Output

1.250000000000

Note

You can see following graphs for sample 1 and sample 3. 

<image> <image>

Solution (in JAVA):

Solution:
import java.util.Scanner;

/**
 * Created by smalex on 17/09/15.
 */
public class P579C {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    int a = scanner.nextInt();
    int b = scanner.nextInt();
    if (a < b) {
      System.out.println(-1);
      return;
    }
    a += b;
    int k = a / (2 * b);
    double res = a / (2.0 * k);
    System.out.println(res);
  }
}