Mate in 39

i.gyazo.com/cfb78cb71315715634f220a20a441b2e.png

i.gyazo.com/9294b242b8e24055b8d62be77df2c2e4.png

I was looking over a game and it asked me to sack the knight and I was wondering why...
Guess we have the answer.
Can anyone do it without a use of a computer?

You should take a look at the variations the engine spits out. After 1....Qh3+ 2.Kxf4 Qh2+ 3.Ke3 (only move) f4+! the white king has to enter the dangerous diagonal 4.Ke4 Qh1+ Skewer -> Queen gone, mate to follow.

For me, Stockfish 8 shows mate in 17, not 39.
1. Qc6 Qh3+ 2. Kxf4 Qh2+ 3. Ke3 f4+ 4. Ke4 Qg2+
5. Kxf4 Qxc6 6. d5 Qc8 7. Bh4 Qf5+ 8. Ke3 Qxe5+
9. Kf2 Qh2+ 10. Ke3 Qxh4 11. Kd4 Qf2+ 12. Ke5 Qf6+
13. Ke4 g3 14. d6 Qf5+ 15. Ke3 g2 16. d7 g1=Q+
17. Kd2 Qff2#