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.util.*;
import java.io.*;

public class A {
    FastScanner in;
    PrintWriter out;

    public void solve() throws IOException {
        int a = in.nextInt();
        int b = in.nextInt();
        if (a < b) {
            out.println(-1);
            return;
        } else if (a == b) {
            out.println(a);
            return;
        }

        double ans1 = 1e10;
        double ans2 = 1e10;
        // /
        int ca = (a - b) / b;
        if (ca % 2 == 1) ca--;
        if (ca != 0) {
            ans1 = ((double) (a - b)) / ca;
        }
        // \
        int bb = ((a + b) / b);
        if (bb % 2 == 1) bb--;
        if (bb != 0) {
            ans2 = ((double) (a + b)) / (double) bb;
        }
        out.println(Math.min(ans1, ans2));
    }

    public void run() {
        try {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
            Locale.setDefault(Locale.US);

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
    }

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