Kth Minimum in Array

Simpl analyzes arrays of payment amounts to identify low-value transactions efficiently. Given an unsorted array of integers, return the kth smallest element, counting duplicate values as separate elements.

Use 1-based indexing for k. The input is guaranteed to contain at least k elements. The function may use additional memory, but should avoid sorting the entire array when a more targeted approach is possible.

Formal Specification

Implement kth_smallest(nums, k):

• Input: nums, a non-empty list of integers, and k, a positive integer.
• Output: The integer that would appear at index k - 1 if nums were sorted in nondecreasing order.
• The original array does not need to be preserved if your approach modifies it.