Kth Smallest Element in a Sorted Matrix

Given an n x n matrix where each of the rows and columns is sorted in ascending order, return the kth smallest element in the matrix.

Note that it is the kth smallest element in the sorted order, not the kth distinct element.

Examples

Example 1:

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

Output: 13

Explanation: The elements in sorted order are [1, 5, 9, 10, 11, 12, 13, 13, 15], and the 8th smallest is 13.

Example 2:

Input: matrix = [[1, 2], [1, 3]], k = 2

Output: 1

Explanation: The elements in sorted order are [1, 1, 2, 3], and the 2nd smallest is 1.

Example 3:

Input: matrix = [[-5]], k = 1

Output: -5

Explanation: There is only one element, so the 1st smallest is -5.

Constraints

• n == matrix.length == matrix[i].length
• 1 <= n <= 300
• -10^9 <= matrix[i][j] <= 10^9
• All rows and columns are sorted in non-decreasing order.
• 1 <= k <= n^2