Connected Subgraph

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 $998\\,244\\,353$.