Permutation

Recall that a permutation of length $$$n$$$ is an array where each element from $$$1$$$ to $$$n$$$ occurs exactly once.

For a fixed positive integer $$$d$$$, let's define the cost of the permutation $$$p$$$ of length $$$n$$$ as the number of indices $$$i$$$ $$$(1 \le i < n)$$$ such that $$$p_i \cdot d = p_{i + 1}$$$.

For example, if $$$d = 3$$$ and $$$p = [5, 2, 6, 7, 1, 3, 4]$$$, then the cost of such a permutation is $$$2$$$, because $$$p_2 \cdot 3 = p_3$$$ and $$$p_5 \cdot 3 = p_6$$$.

Your task is the following one: for a given value $$$n$$$, find the permutation of length $$$n$$$ and the value $$$d$$$ with maximum possible cost (over all ways to choose the permutation and $$$d$$$). If there are multiple answers, then print any of them.