1NT was 15-17, and 2S was natural. 2NT was lebensohl - it could have been lots of different handtypes, but after your forced 3C call, partner's 3NT bid revealed a raise to 3NT with a spade stopper.
LHO leads the king of spades, and you see:
What's your plan here?
First thing's first: Count your tricks. Ace of spades, ace of hearts, ace-king of clubs, and five diamonds add up to the nine tricks you need for 3NT. Great!
Next: Are there any problems that might arise? There's a big one, if you're not careful! Take a closer look at the diamond suit:
You can't run all five tricks due to the blockage in the diamond spots (unless the opposing diamonds break 2-2, which only occurs 40% of the time). Sadly, the defense has just started an assault on the side entry to the long diamond. On a heart lead, you could have won the ace, played four rounds of diamonds ending in your hand, then led to the ace of spades to cash the last diamond. But no use despairing of what could have been... can you see the way around the problem?
Just duck the first two spades! On the ace of spades you can drop one of your big diamond spots and the suit will now look like
Now, king, ace, and queen of diamonds will leave you in the right hand to enjoy the fifth diamond.
What if the defense doesn't do your dirty work for you? An astute West might switch after the first spade. If he switches to a heart, he sets up another trick for you there, so he'd probably lead a club. Win that club, cash two rounds of diamonds ending on the board (you never know-- they might be 2-2 this time) and duck a spade. Win the (likely) club return, lead up to the last diamond honor on the table, discard that offensive high diamond from your hand on the ace of spades, and claim your nine tricks.