UPDATE FROM problem, multiple updates of same row don't seem to work

Here is an example:

CREATE TABLE tablea(
id int PRIMARY KEY,
flag int
);

CREATE TABLE tableb(
aid int REFERENCES tablea(id),
flag int
);

INSERT INTO tablea VALUES(1,0);
INSERT INTO tablea VALUES(2,0);

-- Flags for 1st row of tablea - When ORed, should be 7
INSERT INTO tableb VALUES(1,1);
INSERT INTO tableb VALUES(1,2);
INSERT INTO tableb VALUES(1,4);

-- Flags for 2nd row of tablea - When ORed, should be 5
INSERT INTO tableb VALUES(2,1);
INSERT INTO tableb VALUES(2,4);

UPDATE tablea
SET flag = tablea.flag | tableb.flag
FROM tableb
WHERE tablea.id = tableb.aid;

SELECT * from tablea;
id | flag
----+------
1 | 1
2 | 1

-- Desired output is
id | flag
----+------
1 | 7
2 | 5

Is there a way around this so that I can get the desired output?

--
David Stanaway <david(at)stanaway(dot)net>