Modify the binary search algorithm to take the upper of the two middle array elements in case the input array has even length. In other words, in the binary search algorithm, replace

mid :$={|}_{{?}_{?}}\frac{\text{b}\text{o}\text{t}+\text{t}\text{o}\text{p}}{(2{)}_{{?}_{?}}}|$ with mid :$=|$~$\frac{\text{b}\text{o}\text{t}+\text{t}\text{o}\text{p}}{2}$~$|$

Trace the action of the modified binary search algorithm on the variables index, bot, top, mid, and the given values of $x$ for the input array

$a[1]=$ Ann, $a[2]=$ Dawn, $a[3]=$ Erik, $a[4]=$ Gail, $a[5]=$ Juan, $a[6]=$ Matt, $a[7]=$ Max, $a[8]=$ Rita, $a[9]=$ Tsuji, $a[10]=$ Yuen,

where alphabetical ordering is used to compare elements of the array.

$($a$)x=$ Erik

$\backslash$table$[[$iteration$,0,1,2$