Is there any algorithm to solve the following problem within several seconds? If not, what if $$$1 \le a_i \le 10^9$$$, $$$1 \le b \le 10^9$$$?

You are given an array of integers $$$a_1, a_2, \ldots, a_n$$$ of length $$$n$$$. Then you should process $$$q$$$ queries. In each query, you are given an integer $$$b$$$. How many elements of the array $$$a$$$ are the factors of $$$b$$$?

We say $$$a$$$ is a factor of $$$b$$$, if and only if there exists an integer $$$c$$$ such that $$$a \cdot c = b$$$.

Constraints: $$$1 \le n \le 10^5$$$, $$$1 \le q \le 10^5$$$, $$$1 \le a_i \le 10^{18}$$$, $$$1 \le b \le 10^{18}$$$.

For example, $$$n = 3$$$, $$$a = \{ 4, 6, 17 \}$$$, $$$q = 4$$$:

• $$$b = 12$$$, answer is $$$2$$$.
• $$$b = 34$$$, answer is $$$1$$$.
• $$$b = 102$$$, answer is $$$2$$$.
• $$$b = 40800$$$, answer is $$$3$$$.