You are given an array of \(N\) positive integers and \(Q\) queries. In each query, you are given an index \(i\) \((1\leq i \leq N)\). Find an index \(j\) \((1\leq j \leq N)\) such that \((i\) & \(j) = 0\) and \(A_i + A_j\) is maximum. Find the maximum possible value \(A_i+A_j\) for each query. If no such index \(j\) exists, then the answer is \(-1\).

Note: Here, \(\&\) is a bitwise AND operator.

Input format

• The first line contains \(T\) denoting the number of test cases.
• The first line of each test case contains an integer \(N\) denoting the number of array elements.
• The next line contains \(N\) space-separated positive integers.
• The next line contains an integer \(Q\) denoting the number of queries that must be performed.
• Each of the next \(Q\) lines contains an integer \(i\).

Output format

For each test case, print \(Q\) lines where the \(i^{th}\) line must contain the output for the \(i^{th}\) query.

Constraints

\(1 \leq T \leq 20\)

\(1 \leq N, Q \leq 10^5\)

\(1 \leq A_i \leq 10^9\)

\(1 \leq Q_i \leq N\)