Material to mate - opponent wins on time when impossible to mate

It seems to me in the final position that it is not possible for white to mate even with black's help. I guess that a mate is only possible if the black pawn is on h7, with the black king on h8, the white king on f8 or f7.

So should the correct result be a draw?

Actually - it has just occurred to me that there is a way for white to mate. You can probably see it...

The pawn isn't even needed. Just have black king on A1, black bishop A2, white King c2, then white moves bishop onto the main diagonal for mate

Very true. There's also a way that doesn't involve the white King...

Umm... who will let the other player mate you?

That is the question! :)