H-m-m-m-m.... 
 
I guess white should move their bishop to c5 first to defend pawn and control a7 simultaneously. 
 
1. Kg8 Qa7 2. Bd4 Qb8 (2.. Qxd4 3. b8Q+ +- and due to better position of the white king endgame is won by White) 
3. Bc5! and Black has no moves at all. :-) 
 
3..f5 (f6 takes a little longer) 4. Kg7 (white should wait too) f4 5. Kf6 (to defend pawn on e7 should bishop leave) f3  
 
And... :-) 
 
6. Bf2!! and black is forced to take with queen. 
 
Zugzwang :-) 
 
So, answer is -- 'white wins'. 
 
It is a real pleasure to solve this thing. 
 
Many thanks, Natalia :-)

I've finally found the win  
1.Kg8!!! Qa7 2.Bd4!! Qb8 3.Bc5! f6 4.Kg7! f5 5.Kg6!! f4 6.Kf6 f3 7.Bf2!! Qa7 forced (Qxb7 8.cxb7 and it frees the c-pawn) 8.Bxa7 f2 9.b8/R! mate 
if 3...f5 directly then the King does not go to g6 but directly to f6 and it wins as well.