CF1854E 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.