Kth Smallest Element in Sorted Matrix

**Problem Statement:** Given the required input arguments, write an efficient algorithm to solve the **Kth Smallest Element in Sorted Matrix** problem. Implement the required logic as specified by standard definitions for this classic algorithmic challenge. **Hint / Expected Approach:** Binary search on value range + count elements ≤ mid **Edge Cases to Consider:** - (1) k = 1 - (2) k = n² - (3) Duplicate values in matrix

Examples

Example 1

Input: [[1,5,9],[10,11,13],[12,13,15]], 8

Output: 13

Example 2

Input: [[-5]], 1

Output: -5

Explanation: Single element

Example 3

Input: [[1,2],[3,4]], 2

Output: 2

Constraints

▪Input arguments are within valid ranges
▪Optimize for execution speed
▪Handle null/empty inputs gracefully

Watch Out For Edge Cases

▪k = 1
▪k = n²
▪Duplicate values in matrix

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Binary Search