A14890 | Equal LCM Subsets

You are given two sets of positive integers $A$ and $B$ . You have to find two non-empty subsets $S_A \subseteq A$ , $S_B \subseteq B$ so that the least common multiple (LCM) of the elements of $S_A$ is equal to the least common multiple (LCM) of the elements of $S_B$ .

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 $1000$ .

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.