![\"\"](\"https://assets.leetcode.com/uploads/2022/11/07/max-star-sum-descdrawio.png\")
There is an undirected graph consisting of n nodes numbered from 0 to n - 1. You are given a 0-indexed integer array vals of length n where vals[i] denotes the value of the ith node.
You are also given a 2D integer array edges where edges[i] = [ai, bi] denotes that there exists an undirected edge connecting nodes ai and bi.
A star graph is a subgraph of the given graph having a center node containing 0 or more neighbors. In other words, it is a subset of edges of the given graph such that there exists a common node for all edges.
The image below shows star graphs with 3 and 4 neighbors respectively, centered at the blue node.
\nThe star sum is the sum of the values of all the nodes present in the star graph.
\n\nGiven an integer k, return the maximum star sum of a star graph containing at most k edges.
\n
Example 1:
\n![\"\"](\"https://assets.leetcode.com/uploads/2022/11/07/max-star-sum-example1drawio.png\")
\n\nInput: vals = [1,2,3,4,10,-10,-20], edges = [[0,1],[1,2],[1,3],[3,4],[3,5],[3,6]], k = 2\nOutput: 16\nExplanation: The above diagram represents the input graph.\nThe star graph with the maximum star sum is denoted by blue. It is centered at 3 and includes its neighbors 1 and 4.\nIt can be shown it is not possible to get a star graph with a sum greater than 16.\n\n\n
Example 2:
\n\n\nInput: vals = [-5], edges = [], k = 0\nOutput: -5\nExplanation: There is only one possible star graph, which is node 0 itself.\nHence, we return -5.\n\n\n
\n
Constraints:
\n\nn == vals.length1 <= n <= 105-104 <= vals[i] <= 1040 <= edges.length <= min(n * (n - 1) / 2, 105)edges[i].length == 20 <= ai, bi <= n - 1ai != bi0 <= k <= n - 1给你一个 n 个点的无向图，节点从 0 到 n - 1 编号。给你一个长度为 n 下标从 0 开始的整数数组 vals ，其中 vals[i] 表示第 i 个节点的值。
同时给你一个二维整数数组 edges ，其中 edges[i] = [ai, bi] 表示节点 ai 和 bi 之间有一条双向边。
星图 是给定图中的一个子图，它包含一个中心节点和 0 个或更多个邻居。换言之，星图是给定图中一个边的子集，且这些边都有一个公共节点。
下图分别展示了有 3 个和 4 个邻居的星图，蓝色节点为中心节点。
星和 定义为星图中所有节点值的和。
\n\n给你一个整数 k ，请你返回 至多 包含 k 条边的星图中的 最大星和 。
\n\n
示例 1：
\n\n
输入：vals = [1,2,3,4,10,-10,-20], edges = [[0,1],[1,2],[1,3],[3,4],[3,5],[3,6]], k = 2\n输出：16\n解释：上图展示了输入示例。\n最大星和对应的星图在上图中用蓝色标出。中心节点是 3 ，星图中还包含邻居 1 和 4 。\n无法得到一个和大于 16 且边数不超过 2 的星图。\n\n\n
示例 2：
\n\n输入：vals = [-5], edges = [], k = 0\n输出：-5\n解释：只有一个星图，就是节点 0 自己。\n所以我们返回 -5 。\n\n\n
\n\n
提示：
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