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.*;
import java.util.*;


public class Program {

    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;

    static final int MOD = 1000000007;
    static final double INF = 10000000000.0;
    static final int MAX = 1000001;
    
   
 	void solve() throws IOException {
 		int a, b;
 		a = nextInt();
 		b = nextInt();
 		if (a < b)
 			out.println("-1");
 		else
 			out.printf("%.12f",(double)(a+b)/(2. * ((a+b)/(2 * b))));
    }

    Program() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

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

    String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }

    String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }

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

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

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
    
    class Pair implements Comparable<Pair>{

        int first, second;

        public Pair(int an1, int an2){
            first = an1;
            second = an2;
        }

        @Override
        public int compareTo(Pair o) {
            if (first - o.first == 0)
            	return second - o.second;
            else
            	return first - o.first;
        }
    }
}