A. Array Eliminationtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given array a_1, a_2, \ldots, a_n, consisting of non-negative integers.Let's define operation of "elimination" with integer parameter k (1 \leq k \leq n) as follows:  Choose k distinct array indices 1 \leq i_1 < i_2 < \ldots < i_k \le n.  Calculate x = a_{i_1} ~ \& ~ a_{i_2} ~ \& ~ \ldots ~ \& ~ a_{i_k}, where \& denotes the bitwise AND operation (notes section contains formal definition).  Subtract x from each of a_{i_1}, a_{i_2}, \ldots, a_{i_k}; all other elements remain untouched. Find all possible values of k, such that it's possible to make all elements of array a equal to 0 using a finite number of elimination operations with parameter k. It can be proven that exists at least one possible k for any array a.Note that you firstly choose k and only after that perform elimination operations with value k you've chosen initially.InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \leq t \leq 10^4). Description of the test cases follows.The first line of each test case contains one integer n (1 \leq n \leq 200\,000) — the length of array a.The second line of each test case contains n integers a_1, a_2, \ldots, a_n (0 \leq a_i < 2^{30}) — array a itself.It's guaranteed that the sum of n over all test cases doesn't exceed 200\,000.OutputFor each test case, print all values k, such that it's possible to make all elements of a equal to 0 in a finite number of elimination operations with the given parameter k.Print them in increasing order.ExampleInput
5
4
4 4 4 4
4
13 7 25 19
6
3 5 3 1 7 1
1
1
5
0 0 0 0 0
Output
1 2 4
1 2
1
1
1 2 3 4 5
NoteIn the first test case:  If k = 1, we can make four elimination operations with sets of indices \{1\}, \{2\}, \{3\}, \{4\}. Since \& of one element is equal to the element itself, then for each operation x = a_i, so a_i - x = a_i - a_i = 0.  If k = 2, we can make two elimination operations with, for example, sets of indices \{1, 3\} and \{2, 4\}: x = a_1 ~ \& ~ a_3 = a_2 ~ \& ~ a_4 = 4 ~ \& ~ 4 = 4. For both operations x = 4, so after the first operation a_1 - x = 0 and a_3 - x = 0, and after the second operation — a_2 - x = 0 and a_4 - x = 0.  If k = 3, it's impossible to make all a_i equal to 0. After performing the first operation, we'll get three elements equal to 0 and one equal to 4. After that, all elimination operations won't change anything, since at least one chosen element will always be equal to 0.  If k = 4, we can make one operation with set \{1, 2, 3, 4\}, because x = a_1 ~ \& ~ a_2 ~ \& ~ a_3 ~ \& ~ a_4 = 4. In the second test case, if k = 2 then we can make the following elimination operations:  Operation with indices \{1, 3\}: x = a_1 ~ \& ~ a_3 = 13 ~ \& ~ 25 = 9. a_1 - x = 13 - 9 = 4 and a_3 - x = 25 - 9 = 16. Array a will become equal to [4, 7, 16, 19].  Operation with indices \{3, 4\}: x = a_3 ~ \& ~ a_4 = 16 ~ \& ~ 19 = 16. a_3 - x = 16 - 16 = 0 and a_4 - x = 19 - 16 = 3. Array a will become equal to [4, 7, 0, 3].  Operation with indices \{2, 4\}: x = a_2 ~ \& ~ a_4 = 7 ~ \& ~ 3 = 3. a_2 - x = 7 - 3 = 4 and a_4 - x = 3 - 3 = 0. Array a will become equal to [4, 4, 0, 0].  Operation with indices \{1, 2\}: x = a_1 ~ \& ~ a_2 = 4 ~ \& ~ 4 = 4. a_1 - x = 4 - 4 = 0 and a_2 - x = 4 - 4 = 0. Array a will become equal to [0, 0, 0, 0]. Formal definition of bitwise AND:Let's define bitwise AND (\&) as follows. Suppose we have two non-negative integers x and y, let's look at their binary representations (possibly, with leading zeroes): x_k \dots x_2 x_1 x_0 and y_k \dots y_2 y_1 y_0. Here, x_i is the i-th bit of number x, and y_i is the i-th bit of number y. Let r = x ~ \& ~ y is a result of operation \& on number x and y. Then binary representation of r will be r_k \dots r_2 r_1 r_0, where: r_i = \begin{cases} 1, ~ \text{if} ~ x_i = 1 ~ \text{and} ~ y_i = 1 \\ 0, ~ \text{if} ~ x_i = 0 ~ \text{or} ~ y_i = 0 \end{cases} 
5
4
4 4 4 4
4
13 7 25 19
6
3 5 3 1 7 1
1
1
5
0 0 0 0 0

1 2 4 1 2 1 1 1 2 3 4 5 
['bitmasks', 'greedy', 'math', 'number theory', '*1300']