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:

`stations.length`

will be an integer in range`[10, 2000]`

.`stations[i]`

will be an integer in range`[0, 10^8]`

.`K`

will be an integer in range`[1, 10^6]`

.- Answers within
`10^-6`

of the true value will be accepted as correct.

s