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 $\mathcal{O}(N\sqrt{N}+T)$