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 PYTHON3):

Solution:
import sys

#sys.stdin = open("input.txt")
#sys.stdout = open("output.txt", "w")

x, y = (int(x) for x in input().split())
if y > x:
	print(-1)
elif x == y:
	print(x)
else:
	#first
	k = int((x / y + 1))
	k -= k % 2
	z_first = (x + y) / k
	#print(z_first)
	#second
	k = int((x/y-1))
	k -= k % 2
	if k != 0:
		z_second = (x - y) / k
	else:
		z_second = z_first
	#print(z_second)

	ans = min(z_first, z_second)

	print(ans)