Taman is excited to announce that he has learnt bitwise AND operation. His Big Sister Titly has given him a sequence of non-negative integers x1, x2, . . . , xn as key. To test that whether Taman knows bitwise AND operation or not, Taman is asked to find maximum value among all (a AND xi) where 1 ≤ i ≤ N. But their youngest sister Tamanna is not happy with this. She adds another condition that for a given sequence, Taman has to answer Q queries instead of just one. Can you help poor Taman? Note: Expression x AND y means applying the operation of bitwise AND to numbers x and y. This operation exists in all modern programming languages, for example, in language C++ and Java it is marked as ”&”. Input First line of input will contain the number of test cases, T ≤ 5. Then T test cases follow. First line of each test case contains two integers N (1 ≤ N ≤ 100000) and Q (1 ≤ Q ≤ 30000) separated by a single space. Next line contains N integers x1, x2, . . . , xn separated by a single space (0 ≤ xi < 109). Each of next Q lines describes a query which consists of a single integer a (0 ≤ a < 230). Output For each query output a single integer, the maximum value of (a AND xi) where 1 ≤ i ≤ N. Sample Input 1 33 123 10 11 12 Sample Output 2 3 0