Equal LCM Subsets

Description:

Input:

The input consists of multiple test cases. The first line of the input contains one integer $$$t$$$ ($$$1 \leq t \leq 200$$$), the number of test cases.

For each test case, there is one line containing two integers $$$n, m$$$ ($$$1 \leq n, m \leq 1000$$$), the sizes of the sets $$$A$$$ and $$$B$$$, respectively.

The next line contains $$$n$$$ distinct integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 4 \cdot 10^{36}$$$), the elements of $$$A$$$.

The next line contains $$$m$$$ distinct integers $$$b_1, b_2, \ldots, b_m$$$ ($$$1 \leq b_i \leq 4 \cdot 10^{36}$$$), the elements of $$$B$$$.

The sum of $$$n$$$ for all test cases and the sum of $$$m$$$ for all test cases is at most $$$1000$$$.

Output:

For each test case, if there do not exist two subsets with equal least common multiple, output one line with NO.

Otherwise, output one line with YES, followed by a line with two integers $$$|S_A|, |S_B|$$$ ($$$1 \leq |S_A| \leq n$$$, $$$1 \leq |S_B| \leq m$$$), the sizes of the subsets $$$S_A$$$ and $$$S_B$$$

The next line should contain $$$|S_A|$$$ integers $$$x_1, x_2, \ldots, x_{|S_A|}$$$, the elements of $$$S_A$$$, followed by a line with $$$|S_B|$$$ integers $$$y_1, y_2, \ldots, y_{|S_B|}$$$, the elements of $$$S_B$$$. If there are multiple possible pairs of subsets, you can print any.

Sample Input:

4
3 4
5 6 7
2 8 9 10
4 4
5 6 7 8
2 3 4 9
1 3
1
1 2 3
5 6
3 4 9 7 8
2 15 11 14 20 12

Sample Output:

NO
YES
1 2
6
2 3
YES
1 1
1
1
YES
3 2
3 7 4
12 14