You are given a tree consisting of (n) vertices. Each vertex (i) is painted with a color (c_i). For each distinct color (c) present in the tree, let (m_c) be the total number of vertices of color (c). You are also given an array (k) of length (n), where (k_c) ((1 \le k_c \le m_c)) represents the target component size for color (c). For every color (c) independently, your task is to choose a connected subgraph (a component) consisting of exactly (k_c) vertices. The vertices you choose for the component do not necessarily have to be of color (c). The cost of a chosen component is the sum of the shortest distances from every vertex of color (c) to the chosen component. (The distance from a vertex (v) to a component (S) is defined as the minimum number of edges on a simple path from (v) to any vertex (u) in (S)). For each color (c) from (1) to (n), find the minimum possible cost of a valid component of size (k_c). If there are no vertices of color (c) in the tree, output (-1) for that color. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((1 \le n \le 2 \cdot 10^5)) — the number of vertices in the tree. The second line contains (n) integers (c_1, c_2, \ldots, c_n) ((1 \le c_i \le n)) — the colors of the vertices. The third line contains (n) integers (k_1, k_2, \ldots, k_n) ((1 \le k_i \le n)) — the target component sizes for each color. It is guaranteed that if color (c) appears (m_c \gt 0) times in the tree, then (1 \le k_c \le m_c). Each of the next (n - 1) lines contains two integers (u) and (v) ((1 \le u, v \le n)), representing an edge between vertices (u) and (v). It is guaranteed that the given edges form