Game Bundles
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.
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.
Input
The input is a single integer $m$ ($1 \le m \le 10^{10}$) — the desired number of game bundles.
Output
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.
4
722
1
4
20 20 20 20
15
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
1
60
Note
In the first sample, any subset of size $3$ is a game bundle. There are $4$ such subsets.