Fourier transform $u(s,k)=\frac{2\pi \delta(k-1)}{s(ik+s)}$

Question

Let's say I've given the following function $$u(s,k)=\frac{2\pi \delta(k-1)}{s(ik+s)}$$ Where $\delta(k)$ is the Dirac delta function. I would like to find the inverse Fourier transformation of this one and normally I can easily do the calculations or look up a table or use Maple. But how can I be able to find the inverse by "hand" with respect to $k$?