Neutral Tonality

给定两个序列 $a,b$，将 $b$ 中所有元素以任意顺序在任意位置插入 $a$ 中，使得形成的新序列 $c$ 的最长上升子序列最短，输出你的序列 $c$。

You are given an array $ a $ consisting of $ n $ integers, as well as an array $ b $ consisting of $ m $ integers. Let $ \text{LIS}(c) $ denote the length of the [longest increasing subsequence](https://en.wikipedia.org/wiki/Longest_increasing_subsequence) of array $ c $ . For example, $ \text{LIS}([2, \underline{1}, 1, \underline{3}]) $ = $ 2 $ , $ \text{LIS}([\underline{1}, \underline{7}, \underline{9}]) $ = $ 3 $ , $ \text{LIS}([3, \underline{1}, \underline{2}, \underline{4}]) $ = $ 3 $ . You need to insert the numbers $ b_1, b_2, \ldots, b_m $ into the array $ a $ , at any positions, in any order. Let the resulting array be $ c_1, c_2, \ldots, c_{n+m} $ . You need to choose the positions for insertion in order to minimize $ \text{LIS}(c) $ . Formally, you need to find an array $ c_1, c_2, \ldots, c_{n+m} $ that simultaneously satisfies the following conditions: - The array $ a_1, a_2, \ldots, a_n $ is a subsequence of the array $ c_1, c_2, \ldots, c_{n+m} $ . - The array $ c_1, c_2, \ldots, c_{n+m} $ consists of the numbers $ a_1, a_2, \ldots, a_n, b_1, b_2, \ldots, b_m $ , possibly rearranged. - The value of $ \text{LIS}(c) $ is the minimum possible among all suitable arrays $ c $ .

Each test contains multiple test cases. The first line contains a single integer $ t $ $ (1 \leq t \leq 10^4) $ — the number of test cases. The description of the test cases follows. The first line of each test case contains two integers $ n, m $ $ (1 \leq n \leq 2 \cdot 10^5, 1 \leq m \leq 2 \cdot 10^5) $ — the length of array $ a $ and the length of array $ b $ . 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 elements of the array $ a $ . The third line of each test case contains $ m $ integers $ b_1, b_2, \ldots, b_m $ $ (1 \leq b_i \leq 10^9) $ — the elements of the array $ b $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot 10^5 $ , and the sum of $ m $ over all test cases does not exceed $ 2\cdot 10^5 $ .

For each test case, output $ n + m $ numbers — the elements of the final array $ c_1, c_2, \ldots, c_{n+m} $ , obtained after the insertion, such that the value of $ \text{LIS}(c) $ is minimized. If there are several answers, you can output any of them.

7
2 1
6 4
5
5 5
1 7 2 4 5
5 4 1 2 7
1 9
7
1 2 3 4 5 6 7 8 9
3 2
1 3 5
2 4
10 5
1 9 2 3 8 1 4 7 2 9
7 8 5 4 6
2 1
2 2
1
6 1
1 1 1 1 1 1
777

6 5 4
1 1 7 7 2 2 4 4 5 5
9 8 7 7 6 5 4 3 2 1
1 3 5 2 4
1 9 2 3 8 8 1 4 4 7 7 2 9 6 5
2 2 1
777 1 1 1 1 1 1

In the first test case, $ \text{LIS}(a) = \text{LIS}([6, 4]) = 1 $ . We can insert the number $ 5 $ between $ 6 $ and $ 4 $ , then $ \text{LIS}(c) = \text{LIS}([6, 5, 4]) = 1 $ . In the second test case, $ \text{LIS}([\underline{1}, 7, \underline{2}, \underline{4}, \underline{5}]) $ = $ 4 $ . After the insertion, $ c = [1, 1, 7, 7, 2, 2, 4, 4, 5, 5] $ . It is easy to see that $ \text{LIS}(c) = 4 $ . It can be shown that it is impossible to achieve $ \text{LIS}(c) $ less than $ 4 $ .