Given a tree with $N$ nodes and $N - 1$ edges rooted at node $1$. You have to answer $Q$ queries. In every query, you will be given a node $x$.

Alice will tell his friend Bob the distance from $1$ to $x$. But Bob only knows how to reach a particular distance from $1$. Find the probability that Bob will reach $x$ in one try. If $P$ will be the probability then print $\frac{1}{P}$ in each query.

Note - The distance between two vertices in a tree is equal to the number of edges on the unique simple path between them.

Input Format

• The first line contains $N$ and $Q$ — number of nodes and queries.
• The next  $N-1$ lines follow. The $i^{th}$ line contains two integers $X_i, Y_i$ denoting an edge between the nodes $X_i,Y_i$. It is guaranteed that the given nodes and edges form a tree.
• The next $Q$ lines contain a node $x$.

Output Format

For each query, If $P$ will be the probability to  reach $x$ in one try then print $\frac{1}{P}$ in a separate line.

Constraints

$1 \leq N, Q \leq 10^5 \\ 1 \leq X_i, Y_i \leq N \\ X_i \neq Y_i \\ 1 \leq x \leq N$