Question 4
Let $M$ consist of 2024 positive numbers $a_1,a_2,\ldots,a_{2024}$. For every nonempty subset $T_i$ of $M$, let $s_i$ be the sum of its elements. Prove that all the resulting sums can be partitioned into 2024 nonempty disjoint groups such that the ratio of any two numbers in the same group is at most 2.