Problem A: Reverse Pair

Problem A: Reverse Pair

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 1633  Solved: 314
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Description

In DSAA, we define \((A[i], A[j])\) in array A as a reverse pair iff \(A[i] > A[j]\) and \(i < j\).
Given two non-descending arrays \(A\) with size \(n\) and \(B\) with size \(m\).  
Please return (i) the number of reverse pairs in array \(C=\{A[1], A[2], ..., A[n], B[1], B[2], ..., B[m]\}\);
and  (ii) the non-desending arrary \(C\).

If you do not have any idea, please refer to Page 22 (in lecture 3 slides) for inspiration.


Input

The first line contains an integer T(1 ≤ T ≤10), representing the number of test cases. 

In each test case:

  1. The first line will be two integers \(n\) and \(m\), which are the lengths of the two non decreasing sequences.
  2. The second line will be \(n\) integers\(A_1, A_2, ..., A_n\)
  3. The third line will be \(m\) integers \(B_1, B_2, ..., B_m\)

For all cases, \(1 <= n, m <= 10^5, 0\leq A_i, B_j\leq 10^9\)

Output

For each test case:

  The first line is the number of reverse pairs of \(\{C\}\)

  The second line is sequence \(\{C\}\): \(C_1, C_2, ..., C_{n+m}\)

Sample Input

2
2 4
2 3
1 2 3 4
2 2
3 4
1 2

Sample Output

3
1 2 2 3 3 4 
4
1 2 3 4 

HINT

You may need this. Java FastIO template: https://paste.ubuntu.com/p/6ybMcVXvz5/

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