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 PYTHON):

Solution:
a,b = map(int,raw_input().split())
if a < b:
    print '-1'
    exit(0)
a = float(a)
b = float(b)
left = a - b
right = a + b
dleft = int(left)/(2*int(b))
dright = int(right)/(2*int(b))
try:
    ans_left = left/(2*dleft)
except ZeroDivisionError:
    ans_left = 10**100
try:
    ans_right = right/(2*dright)
except ZeroDivisionError:
    ans_right = 10**100
print '%.9f' %min(ans_left,ans_right)