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.*;
import java.io.*;
public class Main {
public static void main(String [] args)throws Exception{
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	StringTokenizer st = new StringTokenizer(br.readLine());
	int a = Integer.parseInt(st.nextToken());
	int b = Integer.parseInt(st.nextToken());
	
	if(a < b){
		System.out.println("-1");
		return;
	}
	if((a + b) % (2*b) == 0 || (a - b) % (2*b) == 0){
		System.out.println(b);
		return;
	}
	double steps = (a + b)/(2*b);
	double steps1 = (a - b)/(2*b); 
	//System.out.println(steps + " " + (a + b)/(2*steps));
	System.out.println(Math.min((a + b)/(2*steps),(a - b)/(2*steps1)));
}
}