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.

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