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 $a_i \gt b_i$ 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
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
For each test case, output the number of ways to reorder array $a$ such that $a_i \gt b_i$ for all $1 \le i \le n$, modulo $10^9 + 7$.
样例
5
6
9 6 8 4 5 2
4 1 5 6 3 1
3
4 3 2
3 4 9
1
2
1
3
2 3 4
1 3 3
12
2 3 7 10 23 28 29 50 69 135 420 1000
1 1 2 3 5 8 13 21 34 55 89 144
32
0
1
0
13824
题面与样例版权归 Codeforces 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。