Spanning tree problem

Question

I am trying to solve a problem in graph theory that has the following setting: Let $T$ be a forest on the vertex set $\{1,\ldots,n\}$ with components $T_1,\ldots, T_k$. I need to prove that the number of spanning trees on the complete graph on the vertex set $\{1,\ldots,n\}$ that contain $T$ is $n^{k-2}\prod_{i=1}^k |T_i|$. I don't really understand what the spanning tree of a disjoint union of trees on $\{1,\ldots,n\}$ would be. Can someone help me visualise what I am supposed to count?