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.*;
import java.util.*;
public class C579 {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer(br.readLine());
        int a=Integer.parseInt(st.nextToken());
        int b=Integer.parseInt(st.nextToken());
        int x2=a+b;
        /*int k=2;
        double x3=(double)x2/(double)k;
        if(b==0){
            System.out.println("0.000000001");
            return;
        }
        while(x3>=b){
            k+=2;
            x3=(double)x2/(double)k;
        }
        if(k==2)
            System.out.println(-1);
        else
            System.out.println((double)x2/(double)(k-2));*/
        if(b==0){
            System.out.println("0.000000001");
            return;
        }
        int k=(int)((double)x2/(double)b);
        if(k%2!=0)
            k--;
        if(k==0)
            System.out.println(-1);
        else System.out.println((double)x2/(double)k);
    }
}