There exists an undirected tree with n nodes labeled from $0$ to n $- 1$. You are given a $0$ indexed integer array nums of length n, where nums[i] represents the value of the $i^{ ext{th}}$ node. You are also given a positive integer k and a $2 ext{D}$ integer array edges of length n $- 1$, where edges[i] $=$ [u, v] indicates an undirected edge between nodes u and v in the tree.

You can perform the following operation any number of times (including zero times):

• Choose an edge [u, v] connecting nodes u and v.

• Update nums[u] to be nums[u] XOR k.

• Update nums[v] to be nums[v] XOR k.

Return the maximum possible sum of the values of all nodes in the tree after applying the operation any number of times.

Constraints:

• $2 \leq$ n $==$ nums.length $\leq 2 imes 10^4$

• $1 \leq$ k $\leq 10^9$

• $0 \leq$ nums[i] $\leq 10^9$

• edges.length $==$ n $- 1$

• edges[i].length $== 2$

• $0 \leq$ edges[i][0], edges[i][1] $\leq$ n $- 1$

• The input is generated such that edges represents a valid tree.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.