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Large arithmetic progression modulo $p$

Let $B$ be a subset of $Z_p(=\mathbb{Z}/p\mathbb{Z})$ of cardinal $Cp^{\frac{1}{3}}$, for some constant $C$. How to construct an arithmetic progression of length $C_1p^{\frac{2}{3}}$ where $C_1$ is some constant, inside $B+\alpha B$ for any $\alpha \in Z_p$ ?