Maximum-Sum Star with at Most K Arms

Given a simple undirected graph with an integer value on each node and an integer `k`, return the largest node-value sum of any nonempty star subgraph with at most `k` arms. A star has one center and zero or more distinct neighbors selected as leaves. Each selected leaf must be joined to the center by a graph edge. A center alone is a valid star. Count each selected node's value once. The chosen star is a subgraph: any edges between selected leaves need not be included. ### Function and Inputs Complete `bestSumKStar(g_nodes, g_from, g_to, values, k)`: - `g_nodes` is the number of nodes, labeled `0` through `g_nodes - 1`. - `g_from` and `g_to` are equally sized arrays. Edge `i` joins `g_from[i]` and `g_to[i]`. - `values[i]` is the integer value of node `i`. - `k` is the maximum number of arms in the star. Return one integer: the maximum sum among all allowed stars. ### Constraints - `2 <= g_nodes <= 100000` and `1 <= g_edges <= 100000`, where `g_edges` is the length of each edge array. - Every edge endpoint is a valid node label. The graph has no self-loops and at most one edge between a pair of nodes. - `values` has length `g_nodes`, and `-1000 <= values[i] <= 1000`. - `0 <= k <= 100000`. The graph need not be connected. ### Example 1 ```text g_nodes = 4 g_from = [0, 0, 0] g_to = [1, 2, 3] values = [5, 4, -2, 3] k = 2 answer = 12 ``` The star centered at node `0` with leaves `1` and `3` has sum `5 + 4 + 3 = 12`. ### Example 2 ```text g_nodes = 2 g_from = [0] g_to = [1] values = [-4, -1] k = 1 answer = -1 ``` The valid star containing only node `1` has sum `-1`.