Write an efficient algorithm that searches for a value target in an $m**n$ integer matrix. This matrix has the following properties:

a$.$ Integers in each row are sorted in ascending from left to right.

b$.$ Integers in each column are sorted in ascending from top to bottom.

Sample matrix $(2$D array$)$:

$\backslash$table$[[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]]$

Your Algorithm should return a boolean value stating whether the target value exists in the matrix or not in runtime $O(log(n+m)).$

Test Cases:

Input: matrix $=\left[\begin{array}{ccccc}1& 4& 7& 11& 15\\ 2& 5& 8& 12& 19\\ 3& 6& 9& 16& 22\\ 10& 13& 14& 17& 24\\ 18& 21& 23& 26& 30\end{array}\right],$ target $=5$

Output: true

Input: matrix $=\left[\begin{array}{ccccc}1& 4& 7& 11& 15\\ 2& 5& 8& 12& 19\\ 3& 6& 9& 16& 22\\ 10& 13& 14& 17& 24\\ 18& 21& 23& 26& 30\end{array}\right],$ target $=20$

Output: false

Input: matrix $=\left[\begin{array}{ccccc}1& 2& 3& 4& 5\\ 6& 7& 8& 9& 10\\ 11& 12& 13& 14& 15\\ 16& 17& 18& 19& 20\\ 21& 22& 23& 24& 25\end{array}\right],$ target $=6$

Output: true;