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.text.*;
import java.util.*;
public class Main {
	static int a,b,c;
	static double ans;

	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		DecimalFormat ff=new DecimalFormat("0.000000000000");
		a=in.nextInt();b=in.nextInt();
		c=(a+b)/b;if(c%2==1) c--;
		if(c>0) ans=(double)(a+b)/c;
		else if(a>b)
		{
			c=(a-b)/b;if(c%2==1) c--;
			ans=(double)(a-b)/b;
		}
		else ans=-1;
		System.out.println((ans==-1)?-1:ff.format(ans));
	}
}