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1. Kg4 Ke7 2. Kh5 Kf7 3. Kh6 Kf8 (… Ke7 4. Kg7) 4. Kg6 Ke7 5. Kg7 and wins
If BK is on any other square at move 2, then 3. Kg6 leads to a similar win
Basically, the way I think about this is that the white king has to and can get to h6 before the black king can get to g7 closing him out- if white can do that, black can’t stop the loss of the f-pawn. So, Karthik has a winning move with 1.Kg4.
Of course, it probably is a good idea to study the other moves like Ke4 or Ke3. They only draw as can be demonstrated easily:
1. Ke4? Ke7 (Ke8 will draw, too)
2. Kd5 Kd7!
Or
1. Ke3 Ke7 (Ke8 and Kd7 will draw as well)
2. Ke4 Kd6 (Kd8 and Ke8 also draw)
3. Kd4 Kc6! (keeps the white king out of d5)
Of course, the white king is now too far away from g4 to go back that way to win- he is 2 extra moves away from g4, while the black king is only 1 extra move away from g7 compared to the starting position. So, 1.Kg4 is the only winning move.