A11342 | Choose the Different Ones!

Given an array $a$ of $n$ integers, an array $b$ of $m$ integers, and an even number $k$ .

Your task is to determine whether it is possible to choose exactly $\frac{k}{2}$ elements from both arrays in such a way that among the chosen elements, every integer from $1$ to $k$ is included.

For example:

- If $a=[2, 3, 8, 5, 6, 5]$ , $b=[1, 3, 4, 10, 5]$ , $k=6$ , then it is possible to choose elements with values $2, 3, 6$ from array $a$ and elements with values $1, 4, 5$ from array $b$ . In this case, all numbers from $1$ to $k=6$ will be included among the chosen elements.
- If $a=[2, 3, 4, 5, 6, 5]$ , $b=[1, 3, 8, 10, 3]$ , $k=6$ , then it is not possible to choose elements in the required way.

Note that you are not required to find a way to choose the elements — your program should only check whether it is possible to choose the elements in the required way.

The first line of the input contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. The descriptions of the test cases follow.

The first line of each test case contains three integers $n$ , $m$ , and $k$ ( $1 \le n, m \le 2\cdot10^5$ , $2 \le k \le 2 \cdot \min(n, m)$ , $k$ is even) — the length of array $a$ , the length of array $b$ , and the number of elements to be chosen, respectively.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^6$ ) — the elements of array $a$ .

The third line of each test case contains $m$ integers $b_1, b_2, \dots, b_m$ ( $1 \le b_j \le 10^6$ ) — the elements of array $b$ .

It is guaranteed that the sum of values $n$ and $m$ over all test cases in a test does not exceed $4 \cdot 10^5$ .

Output $t$ lines, each of which is the answer to the corresponding test case. As the answer, output "YES" if it is possible to choose $\frac{k}{2}$ numbers from each array in such a way that among the chosen elements, every integer from $1$ to $k$ is included. Otherwise, output "NO".

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.