Pawn Ending I couldn't solve

This ending stumped me!

Each week at the Singapore Chess meetup everyone brings an endgame problem. If it can't be solved by the group in 10 minutes a prize is given. I think I'll present this problem.

At first I tried to race with 1. c7+ Kc8 2. Kc6 a5 but Black's distant passed pawn trumps.

I then looked at 1. Ke6 a5 2. Kf6 a4 3. Kxg6 a4 4. Kxg6 a3 4. Kf7 a2 6. g6 a1=Q 7. g7 Qf1+ 8. Kg6 Qc4 9. Kh7 Qf7 10. Kh8  Qh5+ 11. Kg8 and the King gets in the own way of his pawn.

I conceded that White could not win nor draw this position ...however, can you find a away?

J. Enevoldsen, Skabladet 1953 White to Move