A15573. Maximizing Root

You are given a rooted tree consisting of $n$ vertices numbered from $1$ to $n$ . Vertex $1$ is the root of the tree. Each vertex has an integer value. The value of $i$ -th vertex is $a_i$ . You can do the following operation at most $k$ times.

- Choose a vertex $v$ that has not been chosen before and an integer $x$ such that $x$ is a common divisor of the values of all vertices of the subtree of $v$ . Multiply by $x$ the value of each vertex in the subtree of $v$ .

What is the maximum possible value of the root node $1$ after at most $k$ operations? Formally, you have to maximize the value of $a_1$ .

A tree is a connected undirected graph without cycles. A rooted tree is a tree with a selected vertex, which is called the root. The subtree of a node $u$ is the set of all nodes $y$ such that the simple path from $y$ to the root passes through $u$ . Note that $u$ is in the subtree of $u$ .

The first line contains an integer $t$ ( $1 \leq t \leq 50\,000$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $n$ and $k$ ( $2 \leq n \leq 10^5$ , $0 \leq k \leq n$ ) — the number of vertices in the tree and the number of operations.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 1000$ ), where $a_i$ denotes the value of vertex $i$ .

Each of the next $n - 1$ lines contains two integers $u_i$ and $v_i$ ( $1 \leq u_i, v_i \leq n$ , $u_i \neq v_i$ ), denoting the edge of the tree between vertices $u_i$ and $v_i$ . It is guaranteed that the given edges form a tree.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, output the maximum value of the root after performing at most $k$ operations.

Both examples have the same tree:

For the first test case, you can do two operations as follows:

- Choose the subtree of vertex $4$ and $x = 2$ .  After this operation, the node values become $\{24, 12, 24, 12, 12\}.$
- Choose the subtree of vertex $1$ and $x = 12$ .  After this operation, the node values become $\{288, 144, 288, 144, 144\}.$

The value of the root is $288$ and it is the maximum.For the second test case, you can do three operations as follows:

- Choose the subtree of vertex $4$ and $x = 2$ .  After this operation, the node values become $\{24, 12, 24, 12, 12\}.$
- Choose the subtree of vertex $2$ and $x = 4$ .  After this operation, the node values become $\{24, 48, 24, 48, 48\}.$
- Choose the subtree of vertex $1$ and $x = 24$ .  After this operation, the node values become $\{576, 1152, 576, 1152, 1152\}.$

The value of the root is $576$ and it is the maximum.