You are a Software Engineer at a massive automated warehouse. The warehouse stores crates in a square grid (n x n).

• The Sorting: To save time, the warehouse robots always keep crates sorted: they get heavier as you move Right and heavier as you move Down.
• The Mission: Your manager needs the $k^{th}$ lightest crate in the entire warehouse to fulfill a priority order.

The Technical Hurdle

You could pull all the crates out and sort them in a long line, but that takes too much memory (O(n^2)). The warehouse computer is old—it needs a solution with better memory efficiency.

What You Need to Do

Given an n x n matrix where:

• Each row is sorted in ascending order
• Each column is sorted in ascending order

Return the kᵗʰ smallest element in the matrix.

Function Requirement

Write a function that takes a 2D integer matrix matrix and an integer k, and returns the kᵗʰ smallest element.

Example Case

• Input: matrix = [[1, 5, 9], [10, 11, 13], [12, 13, 15]], k = 8
• Sorted List view: [1, 5, 9, 10, 11, 12, 13, 13, 15]
• 8th Smallest: 13