You are given a tree consisting of N nodes and another integer K, where the \(i^{th}\) node has value equal to \(v[i]\).

Now, we call the value of a sub-tree the number of distinct \(v[i]\) among all nodes it contains. You need to find the number of sub-trees of this tree having value \( \le K \) .

A sub-tree of a tree is a subset of nodes and edges of the tree that form a single connected component.

Input: :

Input starts with an integer \( ( 1 \le T \le 15)\) denoting the number of test cases. Each case starts with two positive integers N and K.

The next line consists of N space separated integers, where the \(i^{th}\) integer denotes \(v[i]\). Each of the next \(N-1\) lines contains 2 space separated integers u and v, denoting an edge between nodes u and v,

Output:

For each test case, print the answer on a new line.

Constraints:

\( 1 \le T \le 15 \)

\( 2 \le N \le 18 \)

\( 1 \le K \le N \)

\( 0 \le v[i] \le 10^9 \)

\( 1 \le u,v \le N \)