Zero-chan has a rooted tree with nodes. The root of given tree is node . She defines .

meas the Least Common Ancestor of node and node .

Zero-chan gives you some integers and asks you to calculate: the number of suffix zeros of

输入描述:

First line contains 2 integers  ( - the size of given tree and the number of queries.

Each of the next  lines contains two integers  () indicating an undirected edge between node  and node . It is guaranteed that the given edges form a tree.

The following line containing  integers describes the queries. Each of query has a integer  ().

输出描述:

For each query, print a integer - the answer of the query.

5 5
2 3
5 4
2 5
1 5
1 2 3 4 5

0
2
1
2
0