CF773C Prairie Partition

It can be shown that any positive integer $ x $ can be uniquely represented as $ x=1+2+4+...+2^{k-1}+r $ , where $ k $ and $ r $ are integers, $ k>=0 $ , $ 0<r

The first line contains a single integer $ n $ ( $ 1

Output, in increasing order, all possible values of $ m $ such that there exists a sequence of positive integers of length $ m $ such that if you replace every element with the summands in its prairie partition and arrange the resulting numbers in non-decreasing order, you will get the sequence given in the input. If there are no such values of $ m $ , output a single integer -1.

In the first example, Alice could get the input sequence from $ [6,20] $ as the original sequence. In the second example, Alice's original sequence could be either $ [4,5] $ or $ [3,3,3] $ .