Overloaded Server in a Two-Stage Routing Scheme

A load balancer routes 4 independent jobs to 3 servers $\{S_1, S_2, S_3\}$. Server $S_1$ already holds one pre-assigned job. Each of the 4 new jobs is routed in two stages: first a coin with $P(\text{heads}) = \tfrac{1}{2}$ is flipped; if heads the job goes to $S_1$, if tails the job is sent to $S_2$ or $S_3$ each with probability $\tfrac{1}{2}$ (i.e., $P(S_2) = P(S_3) = \tfrac{1}{4}$). A server is called "overloaded" if it holds 4 or more jobs (counting the pre-assigned one for $S_1$). Construct the sample space for the 4 routing outcomes and compute $P(\text{at least one server is overloaded})$.