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.math.BigInteger;
import java.util.*;


public class A {

    double INF=1e300;
    double EPS=1e-9;

    void solve() throws IOException {
        double x=nextDouble();
        double y=nextDouble();
        double a=x-y;
        double r1=INF;
        double r2=INF;
        if(a>=0){
            if(a==0)r1=x;
            else{
                double q=a/2;
                if(q>=y){
                    q/=y;
                    int k=(int)Math.floor(q);
                    r1=a/2/k;
                }
            }
        }
        double b=x+y;
        double q=b/2;
        if(q>=y){
            q/=y;
            int k=(int) Math.floor(q);
            r2=b/2/k;
        }
        double result=Math.min(r1,r2);
        if(Math.abs(result-INF)<EPS)
            out.println(-1);
        else
            out.printf(Locale.CANADA,"%.10f\n",result);
    }

    public static void main(String[] args) throws IOException {
        new A().run();
    }

    void run() throws IOException {
        reader = new BufferedReader(new InputStreamReader(System.in));
//      reader = new BufferedReader(new FileReader("input.txt"));
        tokenizer = null;
        out = new PrintWriter(new OutputStreamWriter(System.out));
//      out = new PrintWriter(new FileWriter("output.txt"));
        solve();
        reader.close();
        out.flush();

    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter out;

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
}