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 Main  {

	public static void main(String[] args) {
		Scanner seer = new Scanner(System.in);
		double a = seer.nextInt();
		double b = seer.nextInt();
		if(a < b){
			System.out.println(-1); return;
		}
		double c = (a+b)/2;
		int d = 1; int f = (int)Math.ceil(c+1);
		while(Math.abs(d-f)>1){
			int e = (d+f)/2;
			if(c/(double)e >= b) d = e;
			else f = e;
		}
		System.out.println(c/(double)d);
	}

}