A games programmer is using binary search to search through a large number of moves in a certain game, and suddenly realizes that each of those moves could be made starting from any of the $16$ squares of the game board. In other words, there are now $16$ times as many moves through which to search. What is the maximum number of additional passes that the binary search algorithm might have to make through this larger number of moves to find the move it's looking for?

Question $5$ options:

$4$ times what it was before

Not known, since we don't know what it was before

$16$ more than it was before

$16$ times what it was before

$4$ more than it was before