CF1656H 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.