Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that for any two real numbers $x$ and $y$,
$$|f(x) - f(y)| \leq 7|x - y|^{201}$$
Then,\\
(A) $f(101) = f(202) + 8$\\
(B) $f(101) = f(201) + 1$\\
(C) $f(101) = f(200) + 2$\\
(D) None of the above.