Given a tree with weight assigned to nodes, find out minimum total weight connected component with fixed number of node.
The first line contains a single integer \(n\).
The second line contains \(n\) integers \(w_1, w_2, \ldots, w_n\). \(w_i\) denotes the weight of the node \(i\).
The following \((n - 1)\) lines with two integers \(a_i\) and \(b_i\), which denote the edge between \(a_i\) and \(b_i\).
Note that the nodes are labled by \(1, 2, \ldots, n\).
(\(1 \leq n \leq 2 \cdot 10^3, 1 \leq w_i \leq 10^5\))
\(n\) integers \(c_1, c_2, \ldots, c_n\). \(c_i\) stands for the minimum total weight component with \(i\) nodes.
3 1 2 3 1 2 2 3
1 3 6