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Good game! The two passed pawns decides the game.
A typical remedy in such situations is keeping the rook as active as possible, even by returning some wood. For example (this isn't the only good solution for Black, but pretty convincing) 34...Nxh2 35.Kxh2 Rxf2+ 36.Kg3 Rxb2 37.Rxh7 Rxa2 should win without any trouble.
I feel obliged to post one of the most famous "king walk" games of all time: