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 {
	static Scanner seer = new Scanner(System.in);
	static int a,b;
	public static void main(String[] args) {
		int a = seer.nextInt();
		int b = seer.nextInt();
		if(a < b){
			System.out.println(-1); return;
		}
		double x = minx(a,b);
		System.out.println(Math.min(x,minx(a-2*b,b)));
	}
	public static double minx(int a, int b){
		if(a < b) return Double.MAX_VALUE;
		double x = ((double)(a+b))/2;
		int m = 1; int n = (int)(x+1);
		while(Math.abs(m-n)>1){
			int p = (m+n)/2;
			if((x/p - b) >= 0) m = p;
			else n = p;
		}
		if(x/n - b >= 0) m = n;
		return x/m;
	}


}