Calculation exercize

GM Hikaru Nakamura solves puzzles pretty much every single day. He is extremely fast and precise in his calculations.

Here's a snapshot

He goes super fast for easy puzzles and still calculates at lightning speed more difficult puzzles, which makes it hard to follow sometimes !

Here's a position to calculate  BUT I will provide insights into how the solution works, as well as the puzzle solution, do not worry !!

You have to select candidate moves in the initial position and calculate as much as you can 

White to play and win

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Hints now (SPOILER ALERT)

Well you have 2 main ideas for White. Either 1 Rc1 or 1 Ne7+

Does 1Rc1 work ? 1..Rxc6 2Rxc6 Qxc6 3 Qd8+ Kg7 4 Qxd3 Qc1+ seems drawing. 1 Rc1 does not work .

on 1 Ne7+! where does the black king go ?

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SOLUTION ( SPOILER ALERT #2)

If Black chooses 1..Kh7 White wins by 2 Qxf7+ followed by Qg8#. Which means that Black should go on f8.

WHICH BRINGS THE FINAL POSITION which I will post below as another puzzle

WHITE TO PLAY AND WIN

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the second move by white makes this puzzle special. Did you calculate the solution without any hint ? Congrats. @Hikaru would be proud of you !