Inverse Laplace transform of $$\frac{S}{S^2 + a^2}$$ is

A

$$\frac{e^{at} + e^{-at}}{2}$$

B

$$\frac{e^{at} - e^{-at}}{2}$$

C

$$\frac{e^{at}}{2}$$

D

$$\frac{e^{-at}}{2}$$