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:
// Editorial http://codeforces.com/blog/entry/20368
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Polyline {

    public static void main(String[] args) {
        Kattio io = new Kattio(System.in,System.out);
        long a=io.getInt();
        long b=io.getInt();
        
        if(a<b)io.println("-1");
        else io.println((a+b)/(2.0*((a+b)/(2*b))));
        io.close();
    }
static class Kattio extends PrintWriter {

    public Kattio(InputStream i) {
    super(new BufferedOutputStream(System.out));
    r = new BufferedReader(new InputStreamReader(i));
    }
    public Kattio(InputStream i, OutputStream o) {
    super(new BufferedOutputStream(o));
    r = new BufferedReader(new InputStreamReader(i));
    }

    public boolean hasMoreTokens() {
    return peekToken() != null;
    }

    public int getInt() {
    return Integer.parseInt(nextToken());
    }

    public double getDouble() { 
    return Double.parseDouble(nextToken());
    }

    public long getLong() {
    return Long.parseLong(nextToken());
    }

    public String getWord() {
    return nextToken();
    }



    private BufferedReader r;
    private String line;
    private StringTokenizer st;
    private String token;

    private String peekToken() {
    if (token == null) 
        try {
        while (st == null || !st.hasMoreTokens()) {
            line = r.readLine();
            if (line == null) return null;
            st = new StringTokenizer(line);
        }
        token = st.nextToken();
        } catch (IOException e) { }
    return token;
    }

    private String nextToken() {
    String ans = peekToken();
    token = null;
    return ans;
    }
}
}