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)

if a == b:
    print "%.12f" % a
    exit(0)

if a % b == 0 and int(a/b) % 2 == 1: # it's a top corner
    print "%.12f" % b
    exit(0)


# on an ascending portion
k = int((a-b) / (2.0*b))
if k == 0:
    x = 10**20
else:
    x = (a-b)/(2.0*k)

# on a descending portion
k = int((a+b) / (b+b)) - 1
otherX = (a+b) / (2.0*(k+1.0))

print "%.12f" % min(x, otherX)