#P1742G. Orray

    ID: 7923 远端评测题 2000ms 256MiB 尝试: 0 已通过: 0 难度: (无) 上传者: 标签>bitmasksbrute forcegreedymathsortings*1500

Orray

Description

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, $x_i > y_i$.

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 $2 \cdot 10^5$.

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

Input

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

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

Samples

<div class="test-example-line test-example-line-even test-example-line-0">5</div><div class="test-example-line test-example-line-odd test-example-line-1">4</div><div class="test-example-line test-example-line-odd test-example-line-1">1 2 4 8</div><div class="test-example-line test-example-line-even test-example-line-2">7</div><div class="test-example-line test-example-line-even test-example-line-2">5 1 2 3 4 5 5</div><div class="test-example-line test-example-line-odd test-example-line-3">2</div><div class="test-example-line test-example-line-odd test-example-line-3">1 101</div><div class="test-example-line test-example-line-even test-example-line-4">6</div><div class="test-example-line test-example-line-even test-example-line-4">2 3 4 2 3 4</div><div class="test-example-line test-example-line-odd test-example-line-5">8</div><div class="test-example-line test-example-line-odd test-example-line-5">1 4 2 3 4 5 7 1</div>
8 4 2 1 
5 2 1 3 4 5 5 
101 1 
4 3 2 2 3 4 
7 1 4 2 3 4 5 1