Question: If L is a language accepted by some automaton M, which of the following is (are) true?
I. If M is a nondeterministic finite automaton, then L is accepted by some deterministic finite automaton.
II. If M is a deterministic pushdown automaton, then L is accepted by some nondeterministic pushdown automaton.
III. If M is a nondeterministic pushdown automaton, then L is accepted by some deterministic Turing machine.
A: III only
B: I and II only
C: II and III only
D: I, II, and III
Please eliminate two incorrect options first, then think it step by step and choose the most proper one option.