An unknown array of integers arr containing $n$ elements was used to construct a new array nums. A positive integer $k$ ($k > 0$) was chosen, and two arrays were formed:

• lower, where lower[i] $=$ arr[i] $- k$ for each index $i$

• higher, where higher[i] $=$ arr[i] $+ k$ for each index $i$

The elements of lower and higher were then combined in an arbitrary order to form the array nums of length $2 imes n$.

Given the array nums, reconstruct and return the original array arr. If there are multiple valid answers, return any of them.

Note: The integer $k$ must be strictly positive ($k > 0$).

Constraints:

• $2 imes n =$ nums.length

• $1 \leq n \leq 1000$

• $1 \leq$ nums[i] $\leq 10^9$

• The test cases are generated such that there exists at least one valid array arr.

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