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.*;

public class polyline {
	
	public static void main(String[] args) {
		
		Scanner qwe = new Scanner(System.in);
		
		double a = qwe.nextDouble();
		double b = qwe.nextDouble();
		
		if(b > a) System.out.println("-1");
		else{
			double small = Math.floor((a-b)/b);
			small -= small % 2;
			double smallans = 1e50;
			if(small > 0) smallans = (a-b)/small;
			
			double large = Math.floor((a+b)/b);
			large -= large % 2;
			double largeans = (a+b)/large;
			
			System.out.printf("%.9f\n",Math.min(smallans,largeans));
		}
	
		
		qwe.close();
	}

}