I'd like to clarify the meaning of the structure no tener que + verb.
Suppose I say the following:
No tengo que salir.
Which one of the following does the statement above mean?
I don't have to leave.
I have to not leave.
In the first situation, I am expressing that I don't have to leave meaning that I can stay if I wanted to, whereas in the second situation I am expressing that I have to stay.
In general, my question is which part gets negated, the "have to" or the "verb" that comes after?