In the following grid:

(1) The numbers in each column form an increasing arithmetic sequence
(2) The numbers in each row form an increasing arithmetic sequence
(3) The X's in each spot indicate how many digits are in the number
(4) A is at least 1200
(5) B is at least 2900

+---+---+----+----+----+----+----+----+
|  0| XX|  XX|  XX|  XX|  XX|  XX| XXX|
+---+---+----+----+----+----+----+----+
| XX|XXX| XXX| XXX| XXX| XXX| XXX| XXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX| XXX| XXX| XXX| XXX| XXX| XXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX| XXX| XXX| XXX| XXX|XXXX|XXXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX| XXX| XXX|XXXX|XXXX|XXXX|XXXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX| XXX|XXXX|XXXX|XXXX|XXXX|XXXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX|XXXX|XXXX|XXXX|XXXX|XXXX|XXXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX|   A|XXXX|XXXX|XXXX|XXXX|   B|
+---+---+----+----+----+----+----+----+

Reconstruct the grid.
An analytic solution is preferred.