Where does the black king stand in this specific position? [FEN &quot;7r/pppppKpP/6P1/8/8/8/n7/8 w - - 0 1&quot;]

Assume that the following position was reached in a legal game of chess. In the last 5 moves, no pawn has moved and no pieces were captured. The Black king is invisible – on which square does it stand?
The black king must be on c8.
The white king reached g8 through g6 and h7 before the white pawns arrived on g6-h7. A white knight took the Bc8 from b6; the black queen was also taken by a knight. The black king remained en e8, and the black rook on a8, until a few moves ago.
The last moves were for instance:
[Title &quot;Invisible Black King solution&quot;]
[FEN &quot;r3k1K1/ppppp1pP/6P1/8/8/8/8/2n5 w q - 0 1&quot;]

1. Kh8 Na2 2. Kg8 Nc1 3. Kh8 Na2 4. Kg8 O-O-O+
5. Kf7 Rh8