Flatland Space Stations

Flatland is a country with a number of cities, some of which have space stations. Cities are numbered consecutively and each has a road of length connecting it to the next city. It is not a circular route, so the first city doesn't connect with the last city. Determine the maximum distance from any city to its nearest space station.

Example

There are cities and city has a space station. They occur consecutively along a route. City is unit away and city is units away. City is units from its nearest space station as one is located there. The maximum distance is .

Function Description

Complete the flatlandSpaceStations function in the editor below.

flatlandSpaceStations has the following parameter(s):

int n: the number of cities
int c[m]: the indices of cities with a space station

Returns
- int: the maximum distance any city is from a space station

Input Format

The first line consists of two space-separated integers, and .
The second line contains space-separated integers, the indices of each city that has a space-station. These values are unordered and distinct.

Constraints

There will be at least city with a space station.
No city has more than one space station.

Output Format

Sample Input 0

STDIN   Function
-----   --------
5 2     n = 5, c[] size m = 2
0 4     c = [0, 4]

Sample Output 0

Explanation 0

This sample corresponds to following graphic:

hreasy(5).png

The distance to the nearest space station for each city is listed below:

has distance , as it contains a space station.
has distance to the space station in .
has distance to the space stations in and .
has distance to the space station in .
has distance , as it contains a space station.

We then take .

Sample Input 1

6 6
0 1 2 4 3 5

Sample Output 1

Explanation 1

In this sample, so every city has space station and we print as our answer.