Given two integers n and target, find an array of length n such that:

• The absolute values of the elements form a permutation of the integers from $1$ to n.

• The sum of the elements in the array equals target.

Return the lexicographically smallest array that satisfies these conditions. If no such array exists, return an empty array [].

Note: An array a is lexicographically smaller than an array b of the same length if, at the first index where a and b differ, array a has an element strictly smaller than the corresponding element in b.

Constraints:

• $1 \leq$ n $\leq 10^5$

• $-10^{10} \leq$ target $\leq 10^{10}$

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.