It’s well known in China that algorithms can pass the problem with easily.
You are given a tree with n vertices and n-1 edges . For each vertex ,there is a set initially.
You need to perform operations. For the i-th operation, you are given an edge and let and be the union of them.
Finally, you need to find the number of sets contains for each vertex .

The first line contains two integers .
Each line in the following  lines contains two integers .
The following line contains  integers .

Output one line with  integers, the -th of which indicates the number of sets  contains .

5 6
1 2
1 3
1 4
1 5
4 3 2 1 2 3

5 4 4 4 5