Kth Smallest Element in a Sorted Matrix

You are given an n x n matrix where each of the rows and columns is sorted in ascending order. Your task is to find the kth smallest element in the matrix.

Note: The matrix is guaranteed to have its rows and columns sorted in non-decreasing order. Efficient solutions may use a min-heap to achieve the optimal performance.

inputFormat

The input is given via standard input (stdin).

The first line contains two integers n and k, where n is the dimension of the matrix and k is the order of the smallest element to find (1-indexed).

This is followed by n lines, each containing n space-separated integers, representing the rows of the sorted matrix.

outputFormat

Output a single integer to standard output (stdout) — the kth smallest element in the matrix.## sample

3 8
1 5 9
10 11 13
12 13 15

13