The function $f(x)$ has Fourier transform

$$\tilde{f}(k)=\int_{-\infty}^{\infty} f(x) e^{-i k x} d x=\frac{-2 k i}{p^{2}+k^{2}},$$

where $p>0$ is a real constant. Using contour integration, calculate $f(x)$ for $x<0$. [Jordan's lemma and the residue theorem may be used without proof.]