P4672 [BalticOI 2011] Tree Mirroring (Day2)

Let $T$ be a rooted tree (a connected undirected acylic graph), and let $S$ be a perfect copy of $T$. Construct a new graph by taking the union of $T$ and $S$, and merging the corresponding leaf nodes (but never the root). We call such a graph a tree-mirrored graph.

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对于 $30\%$ 的数据，$3 \le N,M \le 300$。 对于 $60\%$ 的数据，$3 \le N,M \le 3500$。 对于所有数据，$3 \le N,M \le 10^5$。