Given a finite arithmetic sequence of positive integers with some terms removed from the middle, reconstruct the whole sequence.

The task

Consider an arithmetic sequence: a list of positive integers in which the difference between any two successive elements is the same.

2 5 8 11 14 17

Now suppose one or more integers is removed from the sequence, subject to the following constraints:

• The integers removed will be consecutive terms of the sequence.
• The first and last integers in the sequence will not be removed.
• At least three integers will remain in the sequence.

For the above sequence, possible removals include:

2 5 8 14 17  (removed 11)
2 5 17       (removed 8 11 14)
2 14 17      (removed 5 8 11)

Your task: Given one of these partial sequences, reconstruct the original full sequence.

Details

You may assume input is valid (has a solution) and is missing at least one term. All numbers in the sequence will be positive (> 0) integers. The sequence may have a positive or negative difference between terms (i.e. it may be increasing or decreasing). It will not be a constant sequence (e.g. 5 5 5).

Your solution may be a full program or a function. Any of the default input and output methods are acceptable.

Your input and output may be a string (with any reasonable delimiter), a list of strings, or a list of numbers. You may represent the numbers in whatever base is convenient for your language.

Please mention any unusual I/O methods/formats in your submission, so others will be able to test your code more easily.

Test cases

In: 2 5 8 14 17
Out: 2 5 8 11 14 17
In: 2 5 17
Out: 2 5 8 11 14 17
In: 2 14 17
Out: 2 5 8 11 14 17
In: 21 9 6 3
Out: 21 18 15 12 9 6 3
In: 10 9 5
Out: 10 9 8 7 6 5
In: 1 10 91 100
Out: 1 10 19 28 37 46 55 64 73 82 91 100

This is code-golf; the shortest answer in each language wins.