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

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

If no such array exists, return an empty array.

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

 

Example 1:

Input: n = 3, target = 0

Output: [-3,1,2]

Explanation:

The arrays that sum to 0 and whose absolute values form a permutation of size 3 are:

The lexicographically smallest one is [-3, 1, 2].

Example 2:

Input: n = 1, target = 10000000000

Output: []

Explanation:

There are no arrays that sum to 10000000000 and whose absolute values form a permutation of size 1. Therefore, the answer is [].

 

Constraints: