Hello, can anyone share the solution of problem B, F and J.

Update: I know how to solve B. During the contest, I forget to consider some special cases.

This is a problem from ONTAK 2014 and you can find the polish statment here Sumy.

You are given a sequence A = {a₁, a₂, ..., a_n}, every element in A is different.

You should construct another sequence B = {b₁, b₂, ..., b_m} which meets the following conditions:

1. m ≤ n
2. sum of all elements in each subset (there are 2^k subset in total) of B should be different
3. every element in A can be represented as sum of some elements of B

n ≤ 21, 1 ≤ a_i ≤ 10¹⁷

can someone provide some ideas?