Gas stations#4211
Along a circular highway of length , there are gas stations. If a driver wants to refuel at some point along the highway, they can drive to any gas station, where they will be happily served. Of course, if the fuel suddenly runs out entirely, the driver will undoubtedly go to the nearest gas station, even if it means turning back.
Nevertheless, there are occasionally unlucky drivers whose fuel runs out right on the road. Determine the maximum possible distance along the highway to the nearest gas station that such drivers may have to cover on foot.
The first line contains two integers: the length of the highway (1 \le l \le 10^5) and the number of gas stations (1 \le n \le 10^4). The second line contains distinct integers l_i (0 \le l_i < l) — gas station positions.
Print the maximum possible distance along the highway to the nearest gas station, with an accuracy of decimal digit.
Example 1