Counting Nodes with Exactly k Ancestors

You are given a tree (a connected acyclic undirected graph) with n nodes. For each test case, you are required to answer q queries. In each query, you are given an integer k; your task is to determine the number of nodes in the tree that have exactly k ancestors (i.e., nodes at depth k when considering node 1 as the root).

Note that the number of ancestors of the root (node 1) is 0 since it does not have any ancestors.

Input and output should be processed through standard input (stdin) and standard output (stdout) respectively.

inputFormat

The input starts with an integer t (1 ≤ t ≤ 100) representing the number of test cases. Each test case is described as follows:

• The first line contains two integers n (1 ≤ n ≤ 10⁵) and q (1 ≤ q ≤ 10⁵), denoting the number of nodes and the number of queries respectively.
• The next n - 1 lines describe the edges of the tree. Each of these lines contains two integers u and v (1 ≤ u, v ≤ n) representing an edge between nodes u and v.
• The following q lines each contain one integer k (0 ≤ k < n), representing a query.

outputFormat

For each test case, output q lines. Each line should contain the number of nodes with exactly k ancestors (i.e. nodes at depth k), in the same order as the queries appear in the input.

## sample

1
5 3
1 2
1 3
2 4
2 5
0
1
2

1
2
2

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