A16138. Game Bundles

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.

The input is a single integer $m$ ( $1 \le m \le 10^{10}$ ) — the desired number of game bundles.

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.

In the first sample, any subset of size $3$ is a game bundle. There are $4$ such subsets.