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I think this question would be a lot easier if I were able to see the tables for n = 2 to n =5. Having the table for n = 10 is nice for testing though.

In Explaination 1:

385643 x 113400^(-1) (mod 1000000009) = 385643 x 902213412 (mod 1000000009)

how did we come about the "902213412" in the equation??

what is meaning of M and how to find M please explain

what is the meaning of average here ? please explain.