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 PYTHON3):

Solution:
def run1(x, y):
    if x < y:
        return -1;
    cst = (x - y) * 0.5;
    l = 1; r = 1000000001;
    ans = - 1.0;
    while(l <= r):
        m = (l + r) >> 1;
        now = cst / m;
        if now >= y:
            ans = now;
            l = m + 1;
        else:
            r = m - 1;
    return ans;

def run2(x, y):
    cst = (x + y) * 0.5;
    l = 1; r = 1000000001;
    ans = - 1.0;
    while(l <= r):
        m = (l + r) >> 1;
        now = cst / m;
        if( now >= y ):
            ans = now;
            l = m + 1;
        else:
             r = m - 1;
    return ans;

x, y = map(int, input().split());
p = run1(x, y);
q = run2(x, y);

ans = - 1.0;

if(ans < 0 or (p > 0 and p < ans) ):
    ans = p;
if(ans < 0 or (q > 0 and q < ans) ):
    ans = q;
print (ans)