774. Minimize Max Distance to Gas Station

On a horizontal number line, we have gas stations at positions stations[0], stations[1], ..., stations[N-1] , where N = stations.length .

Now, we add K more gas stations so that D , the maximum distance between adjacent gas stations, is minimized.

Return the smallest possible value of D .

Example:

Input:

 stations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], K = 9
Output:

 0.500000

Note:

1. stations.length will be an integer in range [10, 2000] .
2. stations[i] will be an integer in range [0, 10^8] .
3. K will be an integer in range [1, 10^6] .
4. Answers within 10^-6 of the true value will be accepted as correct.