不是很懂 题解 中的某些部分。

比如这一句

For the number of ways to choose their ending vertices, observe that it equals the number of rooted forests with $N$ labeled vertices and $\mid S\mid$ edges such that the set of vertices with a parent is $S$.

给一个我自己翻译的版本，有差错的希望能有高人指正一下。