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Ra1 should do the trick. KxR is met with a White King that just oscillates between c1 and c2 until black is forced to push the g pawn
1. Ra1 is right and white K oscillates between d2 and d3 till black’s neutral moves are finished.
If 1 … Ka3 then 2 Kc3 and white oscillates the king on c3 and c2 while black is forced to advance the a pawn and then the g pawn
If 1 … Kb3 then 2 Kc1 and play proceeds similar to the above…black either advances the a pawn and eventually is forced to take the rook on a1 and get stuck pushing the g pawn by white’s King casing in the black King and blocking the doubled a pawns, or black moves the king to a3 at some point and the same basic result ensues.
White wins.Ra1 if Kxa1 Kc2 and then a5 Kc1 a4 Kc2 a3 Kc1g6 Hxg6 and the pawn will soon be queen and checkmate