Equal LCM Subsets

题面翻译

有两个集合$A,B$，大小分别为$n,m$，你需要找两个非空子集$S_A\subseteq A,S_B\subseteq B$，使得$S_A$中的元素的最小公倍数和$S_B$中的元素的最小公倍数相等。若无解，输出NO，有解输出YES和任意一组解。

多组数据，数据组数$t\leq200,1\leq \sum n,\sum m\leq1000,1\leq a_i,b_i\leq4\times10^{36}$。

题目描述

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 $S_B$ .

输入格式

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 $1000$ .

输出格式

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.

样例 #1

样例输入 #1

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

样例输出 #1

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

请到CF官网提交