Nemotron-IMO-Bench 2026 C46

Prove that for any integer $n>1$ any set $M$ of positive rational numbers with size $2n^2-3n+2$ has a subset $A$ of size $n$ such that for any $k\in \{2,\ldots, n\}$ the sum of any $k$ (not necessarily distinct) numbers from $A$ is not in $A$.