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# 3068. Find the Maximum Sum of Node Values

## Description

There exists an **undirected** tree with `n`

nodes numbered `0`

to `n - 1`

. You are given a **0-indexed** 2D integer array `edges`

of length `n - 1`

, where `edges[i] = [u`

indicates that there is an edge between nodes _{i}, v_{i}]`u`

and _{i}`v`

in the tree. You are also given a _{i}**positive** integer `k`

, and a **0-indexed** array of **non-negative** integers `nums`

of length `n`

, where `nums[i]`

represents the **value** of the node numbered `i`

.

Alice wants the sum of values of tree nodes to be **maximum**, for which Alice can perform the following operation **any** number of times (**including zero**) on the tree:

- Choose any edge
`[u, v]`

connecting the nodes`u`

and`v`

, and update their values as follows:`nums[u] = nums[u] XOR k`

`nums[v] = nums[v] XOR k`

Return *the maximum possible sum of the values Alice can achieve by performing the operation any number of times*.

**Example 1:**

Input:nums = [1,2,1], k = 3, edges = [[0,1],[0,2]]Output:6Explanation:Alice can achieve the maximum sum of 6 using a single operation: - Choose the edge [0,2]. nums[0] and nums[2] become: 1 XOR 3 = 2, and the array nums becomes: [1,2,1] -> [2,2,2]. The total sum of values is 2 + 2 + 2 = 6. It can be shown that 6 is the maximum achievable sum of values.

**Example 2:**

Input:nums = [2,3], k = 7, edges = [[0,1]]Output:9Explanation:Alice can achieve the maximum sum of 9 using a single operation: - Choose the edge [0,1]. nums[0] becomes: 2 XOR 7 = 5 and nums[1] become: 3 XOR 7 = 4, and the array nums becomes: [2,3] -> [5,4]. The total sum of values is 5 + 4 = 9. It can be shown that 9 is the maximum achievable sum of values.

**Example 3:**

Input:nums = [7,7,7,7,7,7], k = 3, edges = [[0,1],[0,2],[0,3],[0,4],[0,5]]Output:42Explanation:The maximum achievable sum is 42 which can be achieved by Alice performing no operations.

**Constraints:**

`2 <= n == nums.length <= 2 * 10`

^{4}`1 <= k <= 10`

^{9}`0 <= nums[i] <= 10`

^{9}`edges.length == n - 1`

`edges[i].length == 2`

`0 <= edges[i][0], edges[i][1] <= n - 1`

- The input is generated such that
`edges`

represent a valid tree.