Kevin has an integer sequence (a) of length (n). At the same time, Kevin has (m) types of magic, where the (i)-th type of magic can be represented by an integer (b_i). Kevin can perform at most (k) (possibly zero) magic operations. In each operation, Kevin can do the following: Choose two indices (i) ((1\leq i\leq n)) and (j) ((1\leq j\leq m)), and then update (a_i) to (a_i\ \&\ b_j). Here, (\&) denotes the bitwise AND operation . Find the minimum possible sum of all numbers in the sequence (a) after performing at most (k) operations. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains three integers (n, m, k) ((1\leq n \leq 10^5), (1\leq m \leq 10), (0\leq k\leq nm)) — the length of (a), the number of types of magic, and the maximum number of operations. The second line contains (n) integers (a_1, a_2, \ldots, a_n) ((0\leq a_i < 2^{30})). The third line contains (m) integers (b_1, b_2, \ldots, b_m) ((0\leq b_i < 2^{30})). It is guaranteed that the sum of (n) over all test cases does not exceed (10^5). For each test case, output one integer — the minimum possible sum of all numbers in the sequence (a) after performing at most (k) operations. In the first test case, one possible way could be: Update (a_1) to (a_1\ \&\ b_1). The sequence will become (5). Update (a_1) to (a_1\ \&\ b_3). The sequence will become (1). In the second test case, one possible way could be: Update (a_1) to (a_1\ \&\ b_3). The sequence will become (1, 6). Update (a_2) to (a_2\ \&\ b_3). The sequence will become (1, 2).