CF1893B.Neutral Tonality

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题目描述

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 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 $c$ .

输入格式

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 $2\cdot 10^5$ .

输出格式

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.

输入输出样例

输入#1

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

输出#1

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

说明/提示

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 $4$ .

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