Directing the Tree

You are given a tree with $N$ nodes, labeled with distinct integers from $1$ to $N$. You are also given $M$ node pairs of the tree, $(a_1, b_1), (a_2, b_2), \dots, (a_M, b_M)$.

Direct every edge of the tree so that for each given pair $(a_i, b_i)$ there is a path from $a_i$ to $b_i$, or a path from $b_i$ to $a_i$. Count the ways to do this. The count can be very large, so print it modulo $10^9 + 7$.

A tree is a graph with $N$ nodes and $N - 1$ edges in which every node has a path to every other node.

The first line contains the number of nodes $N$ and the number of given node pairs $M$ ($1 \le N, M \le 3 \times 10^5$).

Each of the next $N - 1$ lines contains the labels of two nodes joined by an edge.

The $i$th of the next $M$ lines contains two different positive integers $a_i$ and $b_i$, the labels of the nodes in the $i$th pair. All node pairs are mutually different.

Print one line with the number of ways to direct the edges of the tree so that the requirement holds, modulo $10^9 + 7$.