Could you win this endgame?

The position below appeared in Round 5 of the Philadelphia International tournament.  This King and Pawn endgame is a win for Black, but he must play accurately.  Michael Mulyer, an experienced player from Colorado was well up to the task. 

The position of the Kings determines whether or not this position is a win.  For example, if we place White's King on on g3, h4, h5, f4, or f5, then Black can draw.  The method of drawing is to reduce the game to K+P vs K where the defending side can gain opposition.

For Black to win this ending, he must achieve proper King position and force the White King to retreat or give up the remaining Pawn.  If White tries to outflank, Black wins by trading the g Pawn for the h Pawn.  This is what happened in the game.

Using Tablebase, I have pointed out the parts where White had one and only one move that would win.

Could you win this endgame against a chess engine at full strength?   It's not easy. We have to give Mr, Mulyer credit for playing this one so accurately.