Each of A and B is a (base 15) positive integer , with A containing precisely 201 digits and, B containing precisely 202 digits, where:

A = 77…..779 (the digit 7 is repeated precisely 200 times followed by 9), and: B= 77…..779 (the digit 7 is repeated precisely 201 times followed by 9)

Determine the distinct digits in the base 15 representation of A². What are the distinct digits in the base 15 representation of B²?

*** For an extra challenge, solve this puzzle without the help of a computer program.