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Rikka draws a tree with $n$ vertices labeled by $1, 2, \ldots, n$, and adds $k$ extra edges to it. Count the number of ways that she can remove zero or more edges to keep the remaining graph connected, modulo $998\,244\,353$.
The first line contains two integers $n$ and $k$ ($1 \leq n \leq 10^5$, $0 \leq k \leq 10$).
The $i$-th of the following $(n - 1)$ lines contains two integers $a_i$ and $b_i$, which denotes a tree edge between vertices $a_i$ and $b_i$ ($1 \leq a_i, b_i \leq n$). It is guaranteed that these edges form a tree.
The $i$-th of the last $k$ lines contains two integers $u_i$ and $v_i$, which denote an extra edge between vertices $u_i$ and $v_i$ ($1 \leq u_i, v_i \leq n$). It is guaranteed that the resulting graph has no self-loops and no parallel edges.
Print one integer: the number of ways to remove zero or more edges such that the graph remains connected, modulo $998\,244\,353$.
5 1 1 2 2 3 3 4 4 5 1 5
4 2 1 2 2 3 2 4 3 4 1 4