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:
//package codeforcespractice;
import java.io.*;
import java.util.*;
public class problemwithpolyline {
public static void main(String[] args) throws Exception
{
    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    PrintWriter pw=new PrintWriter(System.out);
    StringTokenizer st=new StringTokenizer(br.readLine());
    long a=Long.parseLong(st.nextToken());
    long b=Long.parseLong(st.nextToken());
    double ans=Long.MAX_VALUE;
    long k=(a-b)/(2*b);
    if(k!=0)
    {
        ans=Math.min(ans, ((a-b)*1.0)/(2*k));
    }
    k=(b+a )/(2*b);
    if(k!=0)
    {
        ans=Math.min(ans, ((b+a)*1.0)/(2*k));
    }
    if(ans>=Long.MAX_VALUE)
    {
        pw.println("-1");
    }
    else
    {
        pw.println(ans);
    }
    pw.close();
}
}