Equal LCM Subsets

题意翻译

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 $ .

输入输出格式

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.

输入输出样例

输入样例 #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

输出样例 #1

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