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.Scanner;

//Codeforces 578A
public class Polyline
{
	public static void main(String[] args) 
	{
		Scanner sc = new Scanner(System.in);
		int a = sc.nextInt();
		int b = sc.nextInt();

		if(b>a)
		{
			System.out.println(-1);
			return;
		}
		else if(b==a)
		{
			System.out.println((a+b)/2.0);
		}
		else
		{
			//Existe un answer tal que para todo 1<=k<=answer, se cumple que x/k >= b

			long start = 1;
			long end = 1000000000;
			long answer = end;

			while(end>=start)
			{
				long k = (start+end)/2;
				double actual = (a+b)/(2.0*k);				
				if(actual >= b)
				{
					start = k+1;
					answer = k;
				}
				else
				{
					end = k-1;
				}
			}
			System.out.println((a+b)/(2.0*answer));
		}
	}
}