(P)SQL for a sum with constraints

Hello all,

I have a table with 2 bigint columns, let's call them A and B. I need
a query that will allow me to return A alongside the sum of Bs from
rows where A is less than or equal to this row's A. It is best
described with some example data, consider the following:

A B
1 0
2 1
3 0
4 2
5 1

I want to be able to make a query that returns the following rows:

A funkySumB
1 0
2 1
3 1
4 3
5 4

Anyone have any ideas how to do this? I'm able to do it
programmatically, but it's slow. Optimally I'd like to be able to do
this in the DB. As you can see, it's a little trickier that the usual
aggregate function with a GROUP BY and HAVING.

--
Shug