#100 Maximize AND

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#100 Maximize AND

Authors: woohyunjng

Statement

Statement language

You are given an integer sequence $A = [A_1, A_2, \cdots, A_N]$ of length $N$ .

There are $Q$ queries. Each query gives an integer $X$ . The answer to the query is

\max_{1 \leq i \leq N} (X \mathbin{\&} A_i),

where $\mathbin{\&}$ denotes the bitwise AND operation.

Print the answer to every query. Queries do not modify the sequence $A$ .

The input is given from Standard Input in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

For each test case, print $Q$ lines.

On the $j$ -th line, print $\max_{1 \leq i \leq N}(X_j \mathbin{\&} A_i)$ for the -th query.

#	Score	Constraints
1	17	$N \leq 200$ . $Q \leq 200$ .
2	23	$0 \leq A_i < 2^{10}$ ().

Input

Output

For the query $X=6$ in the first test case, the three values are $6\mathbin{\&}5=4$ , $6\mathbin{\&}2=2$ , and , so the answer is .