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 $S_B$.

Input

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 $1000$.

Output

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.

见题面 Input 部分

见题面 Output 部分