Description:
You are given two arrays $$$a$$$ and $$$b$$$ each consisting of $$$n$$$ integers. All elements of $$$a$$$ are pairwise distinct.
Find the number of ways to reorder $$$a$$$ such that $$$a_i > b_i$$$ for all $$$1 \le i \le n$$$, modulo $$$10^9 + 7$$$.
Two ways of reordering are considered different if the resulting arrays are different.
Input Format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.
The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^{5}$$$) — the length of the array $$$a$$$ and $$$b$$$.
The second line of each test case contains $$$n$$$ distinct integers $$$a_1$$$, $$$a_2$$$, $$$\ldots$$$, $$$a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the array $$$a$$$. It is guaranteed that all elements of $$$a$$$ are pairwise distinct.
The second line of each test case contains $$$n$$$ integers $$$b_1$$$, $$$b_2$$$, $$$\ldots$$$, $$$b_n$$$ ($$$1 \le b_i \le 10^9$$$) — the array $$$b$$$.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^{5}$$$.
Output Format:
For each test case, output the number of ways to reorder array $$$a$$$ such that $$$a_i > b_i$$$ for all $$$1 \le i \le n$$$, modulo $$$10^9 + 7$$$.
Note:
None