H. Equal LCM Subsetstime limit per test10 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputFor 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_BThe 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.ExampleInput
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
Output
NO
YES
1 2
6
2 3
YES
1 1
1
1
YES
3 2
3 7 4
12 14

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

NO YES 1 2 6 2 3 YES 1 1 1 1 YES 3 2 3 7 4 12 14 
['data structures', 'math', 'number theory', '*3200']