Write a function to sort an array of integers with a specific time complexity.
Implement sort_integers(nums) so it returns the integers in nondecreasing order using O(n log n) time. Do not call Python's built-in sorting functions.
Input: A list of integers.
Output: A new list containing the same integers in sorted order.
Example 1: nums = [5, 2, 8, 1] returns [1, 2, 5, 8].
Example 2: nums = [3, 3, -1, 0] returns [-1, 0, 3, 3].
def sort_integers(nums):