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:
def bin_search(tar, mini):
    start = 1
    end = 2000000002
    while(start <= end):
        mid = (start+end)/2
        if tar/mid < mini:
            end = mid-1
            continue
        if tar/(mid+1) < mini: return tar/mid
        start = mid+1
    return float('inf')


def calc(a, b):
    first = bin_search((a+b)/2.0, b)
    second = bin_search((a-b)/2.0, b)
    ans = min(first, second)
    if ans == float('inf'): return -1
    return ans

a, b = map(int, raw_input().split())
print calc(a, b)