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Matrix Median

Problem Description

Given a matrix of integers A of size N x M in which each row is sorted.

Find and return the overall median of matrix A.

NOTE: No extra memory is allowed.

NOTE: Rows are numbered from top to bottom and columns are numbered from left to right.

Problem Constraints

1 <= N, M <= 10^5

1 <= N*M <= 10^6

1 <= A[i] <= 10^9

N*M is odd

Input Format

The first and only argument given is the integer matrix A.

Output Format

Return the overall median of matrix A.

Example Input

Input 1:

```A = [   [1, 3, 5],
[2, 6, 9],
[3, 6, 9]   ] ```

Input 2:

`A = [   [5, 17, 100]    ]`

Example Output

Output 1:

` 5 `

Output 2:

` 17`

Example Explanation

Explanation 1:

```A = [1, 2, 3, 3, 5, 6, 6, 9, 9]
Median is 5. So, we return 5. ```

Explanation 2:

`Median is 17.`

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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