Gas stations

Along the circular highway with a length of $l$ there are $n$ gas stations. If the driver wants to refuel at some point on the highway, he can drive up to any gas station, where he is happy to serve. Of course, if the fuel suddenly runs out completely, the driver will undoubtedly go to the nearest gas station, even if it means turning back.

Nevertheless, occasionally there are unlucky drivers who suddenly run out of fuel right on the road. Determine the maximum possible distance to the nearest gas station that such drivers will have to overcome on foot.

Input

The first line contains two integers: the length of the highway $l(1\le l\le 10^5)$ and the number of gas stations $n(1\le n\le 10^4)$. The second line contains **n** different integers $l_i(0\le l_i<l)$ — the positions of the gas stations.

Output

Print the maximum possible distance to the nearest gas station with an accuracy of $1$ decimal digit.

Examples