conjunctions - "I have no question"--> "Me, too" or "Me, either"?

Ok, at the end of an English class, the teacher says "Do you have any questions?"

Student A: I have no question

Student B: Me, too / Me, either

So, the Student B should say "Me, too" or "Me, either"?

I know that "Me, either" is American English: "Me, either" is American English: Dictionary Link.

EDIT (after comments): So, we can't use "Me, too" in this case?

Note: my question is unique. I know the rule of using "Me, too" or "Me, either". "Me, too" for positive sentence & "Me, either" for negative sentence.

Ex: I have a question. Me, too

Ex2: I don't have a question. Me, either.

So if we say "I have no question" then which one we should use "Me, too" or "Me, either"?

Answer

This is very tricky, and I think this question deserves its own answer.

The best way for Student B to chime in really depends on how Student A answers the initial question:

• 
  

  Student A: I have no question.
  Student B: Me, neither.

  
  


• 
  

  Student A: I don't have any questions.
  Student B: Me, either.

  
  
  


• 
  

  Student A: No questions from me!
  Student B: Me, either.

  
  


• 
  

  Student A: I have some questions.
  Student B: Me, too.

  
  

I'm having a hard time trying to figure out when it's better to use Me, either or Me, neither.