Suppose the two$-$dimensional array A of size $nm$ which is indexed as

$A[0,$dots,$n-1][0,$dots,$m-1]$ contains integers with the property that every

entry is greater than or equal to the entry directly above it and is greater

than or equal to the entry directly to the left of it$.$

An example of such an array is:

$\left[\begin{array}{ccccc}2& 7& 8& 10& 14\\ 3& 8& 9& 11& 15\\ 6& 10& 12& 12& 20\\ 7& 11& 13& 13& 21\\ 8& 11& 15& 20& 22\end{array}\right]$

Write the pseudocode for a function binarysearch$2$d which locates a tar$-$

get entry in the array and returns the location. Your algorithm should

use a $2$D version of binary search.

Hint: In the above example the middle entry is $12.$ If the target is less

than $12$ where could it be$?$ If the target is more than $12$ where could it

be$?$