INTERMEDIATE Puzzle: Mate in Two

1. Qg2 ...
2. Qb3#
Unless black uses moves his bishop and frees up a5. Nethertheless, it's still a quick mate.

@tbuk: I bet you mean Qb7... if Qb7 then Bb6 and it's not mate in two anymore...
@Knightshade: 1. Qg8 then Ka3 and it's not mate in two anymore...

Raito- i said if 1...B moves 2 Qa4#. that means anywhere the bishop moves, 2 Qa4# if mate. just to make you happy, i can write it as 1...Bb6/c7/d8 2 Qa4#.
1. Qa6 then c4 and it's not mate in two anymore...

I coudn't find the solution on my own. What would you say is the underlying idea here?
After looking at the solution I would say the underlying idea is to recognize that any move that black makes weakens his position. So white makes a time wasting move with 1.Bd7 and gives the move back to black. Then any move that black makes is mate in one.
edit: checking this out further, 1.Bd7 isn't purely a time wasting move. It give the white Q another diagonal, for example. OK, is there any underlying idea here, or is it just a matter of recognizing from all the possibilities, the two move combination that get's it done?

@Knightshade: 1. Qg8 then Ka3 and it's not mate in two anymore...
If Qg8 and black moves Ka3, then Qb3 for mate. Still mate in 2.
Furthermore, the solution showing Bd7 does not lead to mate in 2 if black follows by any move other than c4