1742G · Orray

Problem: You are given an array $a$ consisting of $n$ nonnegative integers.

Let's define the prefix OR array $b$ as the array $b_i = a_1~\mathsf{OR}~a_2~\mathsf{OR}~\dots~\mathsf{OR}~a_i$, where $\mathsf{OR}$ represents the bitwise OR operation. In other words, the array $b$ is formed by computing the $\mathsf{OR}$ of every prefix of $a$.

You are asked to rearrange the elements of the array $a$ in such a way that its prefix OR array is lexicographically maximum.

An array $x$ is lexicographically greater than an array $y$ if in the first position where $x$ and $y$ differ, $x_i > y_i$.

Input Format: The first line of the input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ nonnegative integers $a_1, \ldots, a_n$ ($0 \leq a_i \leq 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output Format: For each test case print $n$ integers — any rearrangement of the array $a$ that obtains the lexicographically maximum prefix OR array.