We have learned that Mergesort sorts an array of $n$ numbers in $O$($n

$\backslash$log n$)$$ time and Binary Search determines if a given number is

present in a sorted array of $n$ numbers in $O$(\backslash$log n$)$$ time.

Describe an $O$($n $\backslash$log n$)$$ time algorithm that takes as input two

arrays $A$ and $B$ with $n$ elements each $($not necessarily sorted$)$ and

determines the largest number in $B$ that is not in $A$$.$ If all

elements of $B$ are in $A$$,$ then return $``$All elements of B are in A$\text{'}\text{'}.$

Your algorithm should use mergesort and binary search and should not

use hash tables. Give your algorithm in pseudocode. Justify the

running time of your algorithm.