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:
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import com.sun.jmx.snmp.SnmpDataTypeEnums;
import java.util.Scanner;

public class p3 {
    
    public static void main(String[] args)
    {
        Scanner s=new Scanner(System.in);
        int a=s.nextInt();
        int b=s.nextInt();
        if(b>a || a<0)
        {
            System.out.println(-1);
            return;
        }
        else if(a==b)
        {
          double c=(double)b;
            System.out.printf("%.12f",c);
            System.out.println();
        }
        else
        {
        
            long k1=(a+b)/(2*b);
            long k2=(a-b)/(2*b);
            double x1=(double)(a+b)/(2*k1);
             double x2=(double)(a-b)/(2*k2);
             System.out.printf("%.12f",Math.min(x1,x2));
        
        }
        
    }
    
}