stations is a sorted list of distinct integer positions along a road. You may build k more stations,
each at any integer position. Afterwards, look at the distance between every pair of neighbouring
stations; return the smallest possible value of the largest such distance.
Examples
Input: stations = [1, 13], k = 2
Output: 4
Explanation: build at 5 and 9 -> gaps 4, 4, 4.
Input: stations = [0, 10, 20], k = 1
Output: 10
Explanation: one station cannot shrink both gaps.
Input: stations = [1, 13], k = 1
Output: 6
Constraints
2 <= len(stations) <= 2 * 10**5,0 <= k <= 10**60 <= stations[i] <= 10**9- Required time:
O(n log(max(stations))).
Goals
- Compute how many insertions a gap needs for a given limit with integer arithmetic
- Minimise a maximum by searching the limit