There are (n+m) distinct points ((a_1,0), (a_2,0), \ldots, (a_{n},0), (b_1,2), (b_2,2), \ldots, (b_{m},2)) on the plane. Initially, your score is (0). To increase your score, you can perform the following operation: Choose three distinct points which are not collinear ; Increase your score by the area of the triangle formed by these three points; Then, erase the three points from the plane. Let (k_{\max}) be the maximum number of operations that can be performed. For example, if it is impossible to perform any operation, (k_\max) is (0). Additionally, define (f(k)) as the maximum possible score achievable by performing the operation exactly (k) times . Here, (f(k)) is defined for all integers (k) such that (0 \le k \le k_{\max}). Find the value of (k_{\max}), and find the values of (f(x)) for all integers (x=1,2,\ldots,k_{\max}) independently. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le {3 \cdot 10^4})). The description of the test cases follows. The first line of each test case contains two integers (n) and (m) ((1 \le n,m \le 2 \cdot 10^5)). The second line of each test case contains (n) pairwise distinct integers (a_1,a_2,\ldots,a_{n}) — the points on (y=0) ((-10^9 \le a_i \le 10^9)). The third line of each test case contains (m) pairwise distinct integers (b_1,b_2,\ldots,b_{m}) — the points on (y=2) ((-10^9 \le b_i \le 10^9)). It is guaranteed that both the sum of (n) and the sum of (m) over all test cases do not exceed (2 \cdot 10^5). For each test case, given that the maximum number of operations is (k_{\max}), you must output at most two lines: The first line contains the value of (k_{\max}); The second line contains (k_{\max}) integers denoting (f(1),f(2),\ldots,f(k_{\max})). You are allowed to omit this line if (k_{\max}) is (0). Note that unde