Brother & Sisters! 

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$ \le$i$ \le$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$ \le$5. Then T test cases follow. First line of each test case contains two integers N ( 1$ \le$N$ \le$100000) and Q ( 1$ \le$Q$ \le$30000) separated by a single space. Next line contains N integers x1, x2,..., xn separated by a single space ( 0$ \le$xi < 109). Each of next Q lines describes a query which consists of a single integer a ( 0$ \le$a < 230).

Output 

For each query output a single integer, the maximum value of ( a AND xi) where 1$ \le$i$ \le$N.

Sample Input  

1
3 3
1 2 3
10
11
12

Sample Output  

2
3
0


Problem Setter: Muhammed Hedayet
Alternate Solution: Kazi Rakibul Hossain