The Underground Great Line Network is a grand transit system connecting all corners of Gensokyo. Momoyo noticed that the network's layout resembled a tree(^{\text{∗}}) structure. She couldn't help but imagine the most effective way to dismantle that tree. Given a tree with (n) nodes where node (i) has weight (a_i), select a simple path of exactly (k) edges and remove all edges on it. This splits the tree into (k+1) connected components, each with weight equal to the sum of its nodes' weights. You need to maximize the minimum component weight, or output (-1) if no simple path of exactly (k) edges exists. (^{\text{∗}})A tree is a connected graph without cycles. 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 two integers (n) and (k) ((1 \le k \le n-1), (2 \le n \le 2 \cdot 10^5)). The second line contains (n) integers, where the (i)-th integer represents (a_i) ((1 \le a_i \le 10^9)). The next (n-1) lines each contain two integers (u) and (v), representing an edge of the 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 possible minimum component weight, or (-1) if no such path exists. In the first test case, consider the path (3\to4). Removing this path yields components of weights (6) and (4). In the fourth test case, take the path (1\to2\to5). Removing this path yields components of weights (7), (6), and (9).