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;
public class Main3C {
    public static class Tochka{
        public double a, b, res;
        public Tochka(){
            Scanner scan = new Scanner(System.in);
            a = (double) scan.nextInt();
            b = (double) scan.nextInt();
        }
        public void count(){
            double delta = a-b;
            if( a == b){
                res = a;
                return;
            }
            if( delta > 0){
                int k=100;
                while(delta/(2*k)>=b){
                    k+=100;
                }
                k-=100;
                while(delta/(2*k)>=b){
                    k+=10;
                }
                k-=10;
                while(delta/(2*k)>=b){
                    k+=1;
                }
                k-=1;
                double x1, x2;
                if(k <=(a-b)/b)
                    x1 = delta/(2*k);
                else{
                    res = -1;
                    return;
                }
                k = 100;
                delta = a + b;
                while(delta/(2*k + 2)>=b){
                    k+=100;
                }
                k-=100;
                while(delta/(2*k + 2)>=b){
                    k+=10;
                }
                k-=10;
                while(delta/(2*k + 2)>=b){
                    k+=1;
                }
                k-=1;
                if(k <= (a-b)/b)
                    x2 = delta/(2*k + 2);
                else{
                    res = -1;
                    return;
                }
                
                res = Math.min(x2, x1);
            }   
            else{
                res = -1;
            }
        }
    }
    public static void main(String[] args){
        Tochka a = new Tochka();
        a.count();
        if(a.res == -1){
            System.out.println(-1);
        }
        else{
            System.out.format("%.10f\n", a.res);
        }

    }
}