A15907. Counting Orders

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.

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 $2 \cdot 10^{5}$ .

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 $10^9 + 7$ .