Tree and Colors

There is a tree with $N$ vertices and $N-1$ edges. Vertices are numbered from $1$ to $N$, and the root is vertex $1$. There is exactly one path between any two distinct vertices.

Each vertex has one color, represented by an integer between $1$ and $C$ inclusive. For a vertex $v$ and a color $c$, define the query $f(v, c)$ as follows.

$f(v, c)$ is the number of vertices in the subtree rooted at $v$ whose color is at most $c$.

$M$ queries of the form $f(v_i, c_i)$ are given.

The first line contains $N$, $M$, and $C$ separated by spaces. $N$ is the number of vertices, $M$ is the number of queries, and $C$ is the number of distinct colors, with $1 \le N \le 2 \times 10^5$, $1 \le M \le 2 \times 10^5$, and $1 \le C \le N$.

The second line contains $N$ integers separated by spaces. The $i$-th integer is the color of vertex $i$, and each value is between $1$ and $C$ inclusive.

Each of the following $N-1$ lines describes an edge of the tree. Each line contains two distinct vertex numbers $u$ and $v$ separated by a space, with $1 \le u, v \le N$.

Each of the following $M$ lines describes a query. The $i$-th line contains $v_i$ and $c_i$ separated by a space, with $1 \le v_i \le N$ and $1 \le c_i \le C$.

Print the sum of the answers to all $M$ queries modulo $1,000,000,007$.