can anyone explain me logic for solving this problem not the code only logic part.as the editorial is very confusing

The editorial starts by converting the problem description to some form of mathematical statement.

Do you understand and agree that \{b_1, b_2, ..., b_n\} generates X if and only if gcd(b_1,b_2,...,b_n) divides X?

yes i have understood that part thats because of diophantine equation