Let ~N~ be the maximum of ~B~ over all the cases. We can precompute the number of factors for each number from ~1~ to ~N~ using a method like the Sieve of Eratosthenes. We iterate from ~1~ to ~N~, and for each number we increase the number of factors of all its multiples by 1. The total time complexity is ~N~ times the partial sum for the harmonic series up to ~N~, which can be proven to be ~\mathcal{O}(N \log N)~ in total. Then, for each possible value of ~K~, we can put the number of numbers that have ~K~ as a factor into a list and then we can use binary search on the list associated with a query to answer all the queries. Since a number ~n~ has at most ~2 \cdot \sqrt{n}~ factors, we can also use a prefix sum array here.

Time Complexity: ~\mathcal{O}((N + T) \cdot \log N)~ or ~\mathcal{O}(N \sqrt{N} + T)~