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:
from decimal import Decimal
from decimal import getcontext
getcontext().prec = 50


def bsearch(lo, hi, check):
    while lo < hi:
        mid = lo + ((hi - lo) // 2)
        if check(mid):
            hi = mid
        else:
            lo = mid + 1
    if not check(lo):
        raise ValueError
    return lo



a, b = map(Decimal, raw_input().split())
if a - b == 0:
    print '%.12f' % b
elif a - b < 0:
    print -1
elif a - b > 0:
    t = 0
    x = y = float('inf')
    try:
        kx = (a - b) / Decimal(2.0)
        x = kx / Decimal(-1 + bsearch(1, 10**30, lambda k: (kx / k  < b)))
    except:
        t += 1
    try:
        ky = (a + b) / Decimal(2.0)
        y = ky / Decimal(-1 + bsearch(1, 10**30, lambda k: (ky / k  < b)))
    except:
        t += 1
    if t == 2:
        print -1
    else:
        print "%.12f" % min(x, y)