Results with leading zero

I have a table

CREATE TABLE problem (
problem_id integer,
solution_count integer
);

INSERT INTO problem VALUES (1001, 4);
INSERT INTO problem VALUES (1012, 11);

SELECT * from problem;

problem_id | solution_count
------------+---------------
1001 | 4
1012 | 11
(2 rows)

Is there a way I could write a query to produce the following? I will
need the leading zero for solution < 10

problem_id | solution
-------------+------------
1001 | 01
1001 | 02
1001 | 02
1001 | 04
1012 | 01
1012 | 02
1012 | 03
1012 | 04
1012 | 05
1012 | 06
1012 | 07
1012 | 08
1012 | 09
1012 | 10
1012 | 11
(15 rows)

Thanks.