You are given (n) integers (a_1,a_2,\ldots,a_n) within the range ([0,2^{30})). You can spend (1) coin to increase any (a_i) by (1). You can perform this operation any number of times. You need to solve (q) queries; for each query, you are given an integer (c), also in the range ([0,2^{30})). You would like it if there exists a sequence (b) of length (n) with the following properties: For every (1\le i\le n), (0\le b_i\le a_i). (b_1\oplus b_2\oplus\ldots\oplus b_n=c), where (\oplus) denotes the bitwise XOR operation . Please calculate the minimum number of coins you will have to spend, such that there exists a suitable (b). The queries are independent , meaning that any operations you perform on the sequence (a) will not impact future queries. 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 consists of two integers (n,q) ((1\le n\le5\cdot10^5), (1\le q\le5\cdot10^4)) — the length of sequence (a) and the number of queries. The second line of each test case contains (n) integers (a_1,a_2,\ldots,a_n) ((0\le a_i<2^{30})) — the initial sequence (a). Each of the next (q) lines contains a single integer (c) ((0\le c<2^{30})) — the target XOR. It is guaranteed that the sum of (n) over all test cases does not exceed (5\cdot10^5). It is guaranteed that the sum of (q) over all test cases does not exceed (5\cdot10^4). For each query, output a single integer — the minimum coins you will have to spend, such that there exists a suitable (b). In the first test case, we spend (1) coin to increase (a_2) by (1), resulting in sequence (5,8). A suitable (b) would be (1,8). It can be shown one cannot spend less than (1) coin to achieve the objective. In the second test