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 = [int(x) for x in raw_input().split()]

##if a < b:
##    print -1
##else:
##    t1, t2 = a + b, a - b
##    n1, n2 = t1 // 2 // b, t2 // 2 // b
##    x = -1
##    if n1 > 0:
##        x = float(t1) / n1 / 2
##    if n2 > 0:
##        x = min(x, float(t2) / n2 / 2)
##    else:
##        assert n1 > 0
##    print x

if a < b:
    print -1
elif a < 3 * b:
    t = a + b
    n = t // 2 // b
    print "%.12f" % (float(t) / n / 2)
else:
    t1, t2 = a + b, a - b
    n1, n2 = t1 // 2 // b, t2 // 2 // b
    print "%.12f" % min(float(t1) / n1 / 2, float(t2) / n2 / 2)