Doran's Ring give you more AP damage in your Leap(Q),Empower(W) and the third attack, and also Doran's Ring passive give you more physical damage to minions, helping to farm.
Rushing Nashor's Tooth is great with Conqueror Rune, because you need to rush attack speed to deal more true damage in only 3 seconds of the rune, also Nashor's Tooth give you good stats on a early game like:

50% Attack Speed
80% AP
Passive: Deal more magic damage in basic attacks.

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Then you go Trinity Force and then Hextech Gunblade.
I'm testing that sh*t and i'm getting a win streak on top of 6 matches versus op champs.