Let $p$ and $q$ be two polynomials such that

$$q(z)=\prod_{l=1}^{m}\left(z-\alpha_{l}\right)$$

where $\alpha_{1}, \ldots, \alpha_{m}$ are distinct non-real complex numbers and $\operatorname{deg} p \leqslant m-1$. Using contour integration, determine

$$\int_{-\infty}^{\infty} \frac{p(x)}{q(x)} e^{i x} d x$$

carefully justifying all steps.