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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class A {

    static StringTokenizer st;
    static BufferedReader br;
    static PrintWriter pw;
    
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        long a = nextLong();
        long b = nextLong();
        long k = (a+b) / b / 2;
        boolean ans = false;
        double x = 1e18;
        if (a+b >= 2*k*b && k > 0) {
            x = (a+b) / (2.0*k);
            ans = true;
        }
        k = (a-b) / b / 2;
        if (a-b >= 2*k*b && k > 0) {
            x = Math.min(x, (a-b) / (2.0*k));
            ans = true;
        }
        else if (a==b) {
            ans = true;
            x = Math.min(x, a);
        }
        if (!ans)
            System.out.println(-1);
        else
            System.out.println(x);
        pw.close();
    }

    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    private static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    private static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    private static String next() throws IOException {
        while (st==null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
}