Description:
Rishi is developing games in the 2D metaverse and wants to offer game bundles to his customers. Each game has an associated enjoyment value. A game bundle consists of a subset of games whose total enjoyment value adds up to $$$60$$$.
Your task is to choose $$$k$$$ games, where $$$1 \leq k \leq 60$$$, along with their respective enjoyment values $$$a_1, a_2, \dots, a_k$$$, in such a way that exactly $$$m$$$ distinct game bundles can be formed.
Input Format:
The input is a single integer $$$m$$$ ($$$1 \le m \le 10^{10}$$$) — the desired number of game bundles.
Output Format:
The first line should contain an integer $$$k$$$ ($$$1 \le k \le 60$$$) — the number of games.
The second line should contain $$$k$$$ integers, $$$a_1, a_2, \dots, a_k$$$ ($$$1 \le a_1, a_2, \dots, a_k \le 60$$$) — the enjoyment values of the $$$k$$$ games.
Note:
In the first sample, any subset of size $$$3$$$ is a game bundle. There are $$$4$$$ such subsets.