Nemotron-IMO-Bench 2026 C7

Let $S$ be the set of sequences of length 2018 whose terms are in the set $\{1, 2, 3, 4, 5, 6, 10\}$ and sum to 3860. Prove that $$|S|\leq 2^{3860} \cdot \left(\frac{2018}{2048}\right)^{2018}.$$