You are given a positive integer A. The goal is to construct the shortest possible sequence of integers ending with A, using the following rules

the first element of the sequence is 1,each of the successive elements is the sum of any two preceding elements (adding a single element to itself is also permissible),
each element is larger than all the preceding elements; that is, the sequence is increasing.

For example, for A = 42, a possible solutions is [1, 2, 3, 6, 12, 24, 30, 42]. Another possible solution is [1, 2, 4, 5, 8, 16, 21, 42].