CF1827A 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 $ .