Apply information associated to a large range to a separate document with a smaller range

I apologize for the vague title. I could not find an easy way to describe this dilemma.

Basically what I am trying to do is apply TEXT which is associated with a large data range
E.g TABLE A

to	from	code
0	22	AAAA
22	40	BBBB

To a table with a smaller data range.
e.g TABLE B

to	from	Code from Table A
0	6
6	19
19	22
22	36
30	40

Therefore rows 2-4 on Table B should receive "AAAA" and rows 5-6 should get "BBBB"

The data range breaks between Table A and Table B should line up 95%+ of the time so I do not mind going through manually and fixing the errors to which multiple codes would apply to an interval in Table B.

If anyone has a forumla, macro or any tips for this please let me know!