Lexicographically Smallest Negated Permutation that Sums to Target

Description

You are given a positive integer n and an integer target.

Return the lexicographically smallest array of integers of size n such that:

- The sum of its elements equals target.

- The absolute values of its elements form a permutation of size n.

If no such array exists, return an empty array.

A permutation of size n is a rearrangement of integers 1, 2, ..., n.