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.IOException;
import java.io.InputStreamReader;
import java.util.Locale;
import java.util.StringTokenizer;

public class Main {
	static long a,b, n;
	static double h;
	public static void main(String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer(br.readLine());
		a=Long.parseLong(st.nextToken());
		b=Long.parseLong(st.nextToken());
		if(b > a){
			System.out.println(-1);
			return;
		}
		if (a==b) {System.out.println(a);return;}
		n = b + a;
		h=n/2.0;
		double res1=h/bs(1, n);
		n = a-b;
		h=n/2.0;
		if (a<3*b){System.out.printf(Locale.US,"%.12f\n",res1);return;}
		double res2=h/bs(1, n);
		System.out.printf(Locale.US,"%.12f\n",Math.min(res1, res2));
	}
	private static double bs(long l, long r) {
		if(r <= l) return r;
		long middle = (l+r+1)/2;
		if( (h/middle)>=b) return bs(middle, r);
		else return bs(l, middle-1);
	}
}