C. Optimal Insertiontime limit per test3 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given two arrays of integers a_1, a_2, \ldots, a_n and b_1, b_2, \ldots, b_m.You need to insert all elements of b into a in an arbitrary way. As a result you will get an array c_1, c_2, \ldots, c_{n+m} of size n + m.Note that you are not allowed to change the order of elements in a, while you can insert elements of b at arbitrary positions. They can be inserted at the beginning, between any elements of a, or at the end. Moreover, elements of b can appear in the resulting array in any order.What is the minimum possible number of inversions in the resulting array c? Recall that an inversion is a pair of indices (i, j) such that i < j and c_i > c_j.InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \leq t \leq 10^4). Description of the test cases follows.The first line of each test case contains two integers n and m (1 \leq n, m \leq 10^6).The second line of each test case contains n integers a_1, a_2, \ldots, a_n (1 \leq a_i \leq 10^9).The third line of each test case contains m integers b_1, b_2, \ldots, b_m (1 \leq b_i \leq 10^9).It is guaranteed that the sum of n for all tests cases in one input doesn't exceed 10^6. The sum of m for all tests cases doesn't exceed 10^6 as well.OutputFor each test case, print one integer — the minimum possible number of inversions in the resulting array c.ExampleInput
3
3 4
1 2 3
4 3 2 1
3 3
3 2 1
1 2 3
5 4
1 3 5 3 1
4 3 6 1
Output
0
4
6
NoteBelow is given the solution to get the optimal answer for each of the example test cases (elements of a are underscored).  In the first test case, c = [\underline{1}, 1, \underline{2}, 2, \underline{3}, 3, 4].  In the second test case, c = [1, 2, \underline{3}, \underline{2}, \underline{1}, 3].  In the third test case, c = [\underline{1}, 1, 3, \underline{3}, \underline{5}, \underline{3}, \underline{1}, 4, 6]. 
3
3 4
1 2 3
4 3 2 1
3 3
3 2 1
1 2 3
5 4
1 3 5 3 1
4 3 6 1

0 4 6 
['data structures', 'divide and conquer', 'dp', 'greedy', 'sortings', '*2300']