Kitty's Calculations on a Tree

Kitty has a tree $T$, consisting of $n$ nodes where each node is uniquely labeled from $1$ to $n$. Her friend Alex gave her $q$ sets, where each set contains distinct nodes. Kitty needs to calculate the following expression on each set:

where:

• $\{u,v\}$ denotes an unordered pair of nodes belonging to the set.

• $dist(u,v)$ denotes the number of edges on the unique (shortest) path between nodes $u$ and $v$.

Given $T$ and $q$ sets of $k$ distinct nodes, calculate the expression for each set. For each set of nodes, print the value of the expression modulo $10^9+7$ on a new line.

Input

The first line contains two integers: the number $n(1\le n\le 2\cdot 10^5)$ of nodes in tree $T$ and $q(1\le q\le 10^5)$ — the number of nodes in the query set.

Each of the $n-1$ subsequent lines contains two integers $a$ and $b(1\le a,b\le n)$, that describe an undirected edge between nodes $a$ and $b$.

The $2\cdot q$ subsequent lines define each set over two lines in the following format:

• The first line contains an integer $k$ — the size of the set;

• The second line contains $k$ integers, the set's elements $(1\le k_i\le 10^5$, the sum of $k_i$ over all $q$ does not exceed $2\cdot 10^5)$.

Output

Print $q$ lines where each line $i$ contains the expression for the $i$-th query, modulo $10^9+7$.

Examples