The triangle problem
You wrote the paper, did the main research, hence your name should go first.

The interns contribution is crucial to this paper, she/he helped a lot, but was not so much involved in the writing process? Name her/him second.

Professor B help a lot with constructing the paper, writing, rewriting, reviewing, etc. Put her/him second to last. Indicate her/him as correspondence author, too.

Since professor A is the main initiator, I assume that the research you did is within his field. He might therefore be also the main correspondence author. He will probably also handle submission and other formalities with the journal. Put him last.   

Final Order:
You, Intern C, Professor B,* and Professor A.*

In any way, the person who will handle the submission process, will probably also review this. Don't think too much about the order. In many cases it does not really matter, and most professors do not care too much about this, as they are usually named as correspondence authors anyway.