I think Kh1 would also work because you'd still be off of the first rank when the pawn promotes...
3 legal move only one wins
Also, I just checked and I think Kf1 works as well because you get to c1 faster than the black pawn can.
Also, I just checked and I think Kf1 works as well because you get to c1 faster than the black pawn can.
Kh1 and Kf1 are good enough for a draw but only Kh2 wins as required!
Miraculously, the position is just legal. The black pawns captured all of the missing white units!

Also, I just checked and I think Kf1 works as well because you get to c1 faster than the black pawn can.
Even tho you can catch the pawn, it would be stalemate
made this on my own it isn't that hard