Naaa… I have the complete solution for it… it isn’t using this concept…but it was very nice…only need to optimize the constants in Big O notation
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So you discussed all the details about FFT rather discussing the details about your problem? Man!
Bruh this editorial is used to learn multipoint evaluation. It was written in the time when even blogs on fft were rare.
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Yeah. I see now. I didn’t notice the date.
I am really sorry though. 
Another thing, I am really having trouble to visualize the solution here. Can you please explain why do we take 3 polynomial here and what is it going on when we are combining three polynomials into the answer?
Thanks a lot.