Let A be an n $\backslash$times m matrix of integers, where all elements within a row are in ascending order $($from left to right$),$ and all elements in a column are in ascending order $($from top to bottom$).$ Present an efficient algorithm that determines the position of the integer x in A$,$ i$.$e$.,$ the row and column indices $($i$,$ j$)$ such that Aij $=$ x if x is in A but returns $(-1,-1)$ otherwise.

Example: For the $3\backslash$times $4$ matrix

A $=[[9,21,72],$

$[13,25,72],$

$[15,27,80],$

$[19,37,82]]$

the algorithm returns $(2,3)$ if x $=27$ but returns $(-1,-1)$ if x $=42.$

Provide pseudocode for the algorithm, briefly explain how it works, and justify that its time complexity is $\backslash$Theta $($n $+$ m$).$