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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;


public class AProblemAboutPolyline {
    public static void main(String[] args)throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int a, b;
        a = Integer.parseInt(st.nextToken());
        b = Integer.parseInt(st.nextToken());
        
        if(b>a)
            System.out.println("-1");
        else{
            int aux = (a-b)/(2*b);
//          System.out.println(aux);
            int k = 2*aux+1;
//          System.out.println(k);
            double x = (a-b)%(2*b)/(double)(k+1);
//          System.out.println(x);
            System.out.println((b+x));
        }
        
    }
}