Multi Merge $....................................................................[15]$ Consider the following slight variant of the Merge procedure we saw in class. The inputs are two sorted arrays of integers, B$,$C$.$ Important technical note: As discussed in class, we use the convention that accessing an out$-$of$-$bounds index returns $\backslash$infty $.$

Algorithm $3$ Procedure Merge$($B$,$C$)$

$1$: Initialize A to be the empty vector

$2$: Define i $=0,$ j $=0,$ n $=|$B$|+|$C$|$

$3$: for t $=0,...,$n $1$ do

$4$: if B$[$i$]<=$ C$[$j$]$ then

$5$: append B$[$i$]$ to A

$6$: increment i

$7$: else

$8$: append C$[$j$]$ to A

$9$: increment j

$10$: end if

$11$: end for

$($a$)[2]$ If B and C are two arrays of not$-$necessarily$-$equal length, argue $($with $2-3$ lines of reasoning$)$ that the Merge function takes time O$(|$B$|+|$C$|).$