Erdős Problem #337 — For a set $A$, let $A_m(x)$ denote $\left| \{ a_{i_1} + \ldots + a_{i_m} : a_{i_k} \in A \} \cap \{1, \ldots, x\} \right|$.

For a set $A$, let $A_m(x)$ denote $\left| \{ a_{i_1} + \ldots + a_{i_m} : a_{i_k} \in A \} \cap \{1, \ldots, x\} \right|$. If $A$ is a basis and $A_1(x) = o(x)$ is it true that

$$\lim_{x \to \infty} \frac{A_2(x)}{A_1(x)} = \infty \ ?$$