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 static java.lang.Math.*;
import static java.lang.System.currentTimeMillis;
import static java.lang.System.exit;
import static java.lang.System.arraycopy;
import static java.util.Arrays.sort;
import static java.util.Arrays.binarySearch;
import static java.util.Arrays.fill;
import java.util.*;
import java.io.*;

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

    BufferedReader in;
    PrintWriter out;
    StringTokenizer st = new StringTokenizer("");

    private void run() throws IOException {
        if (new File("input.txt").exists())
            in = new BufferedReader(new FileReader("input.txt"));
        else
            in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        in.close();
        out.close();
    }
    
    final int N = 1000 * 1000;
    
    final double EPS = 1e-13;
    
    private void solve() throws IOException {
        
        int a = nextInt();
        int b = nextInt();
        
        if (b > a) {
            out.println(-1);
            return;
        }
        
        int k = (a - b) / (b * 2);
        
        double l = b;
        double r = l * 2;
        
        double da = a;
        double db = b;
        double ds = da + db;
        
//      while (((r - l > EPS))) {
        while (!((r - l < EPS) || ((r - l) / (r + l)) < EPS)) {
            
            double m = (l + r) / 2.;
            double x = (2 * k + 2) * m;
            if (x < ds)
                l = m;
            else
                r = m;
        }
        
        out.printf(Locale.US, "%.12f", l);
        
        
    }
    
    void chk(boolean b) {
        if (b)
            return;
        System.out.println(new Error().getStackTrace()[1]);
        exit(999);
    }
    void deb(String fmt, Object... args) {
        System.out.printf(Locale.US, fmt + "%n", args);
    }
    String nextToken() throws IOException {
        while (!st.hasMoreTokens())
            st = new StringTokenizer(in.readLine());
        return st.nextToken();
    }
    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 nextLine() throws IOException {
        st = new StringTokenizer("");
        return in.readLine();
    }
    boolean EOF() throws IOException {
        while (!st.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null)
                return true;
            st = new StringTokenizer(s);
        }
        return false;
    }
}