(Fermat 2023, Part B, Question 15, CEMC - UWaterloo)

A sequence has $101$ terms, each of which is a positive integer. If a term, $n$, is even, the next term is equal to $\frac{1}{2} n + 1$. If a term, $n$, is odd, the next term is equal to $\frac{1}{2}(n + 1)$. For example, if the first term is $7$, then the second term is $4$ and the third term is $3$. If the first term is $16$, the $101st$ term is
$(A)$ $1$
$(B)$ $2$
$(C)$ $3$
$(D)$ $4$
$(E)$ $5$

Answer Submission Note(s)
Your answer should be a single capital letter, e.g. 'A'.