E. Game Bundlestime limit per test3 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputRishi 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.InputThe input is a single integer m (1 \le m \le 10^{10}) — the desired number of game bundles.OutputThe 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.ExamplesInput
4
Output
4
20 20 20 20
Input
722
Output
15
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1Input
1
Output
1
60
NoteIn the first sample, any subset of size 3 is a game bundle. There are 4 such subsets.
4

4 20 20 20 20 
['brute force', 'constructive algorithms', 'dp', 'greedy', 'math', '*3000']