Given a positive integer $$$n$$$, we say that a positive integer $$$x$$$ is $$$n$$$-mersenne if and only if $$$2^x - 1$$$ divides $$$2^n - 1$$$.
Find all $$$n$$$-mersenne positive integers.
The first line of input contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$), the number of test cases.
Each test case contains one line of one integer $$$n$$$ ($$$1 \le n \le 10^9$$$), the integer described in the problem.
For each test case containing an integer $$$n$$$, let $$$x_1, x_2, \dots, x_k$$$ (for some positive integer $$$k$$$) be all distinct $$$n$$$-mersenne positive integers where $$$x_1 \lt x_2 \lt \dots \lt x_k$$$. Output $$$x_1, x_2, \dots, x_k$$$ space-separated in ascending order.
It is guaranteed that the sum of $$$k$$$ over all test cases would not exceed $$$2 \cdot 10^6$$$.
3 1 4 6
1 1 2 4 1 2 3 6
In the first test case, we note that $$$2^1 - 1 = 1$$$, and only $$$1$$$-mersenne number if $$$1$$$ itself.
In the second test case, we note that $$$2^4 - 1 = 15$$$, and the divisors of $$$15$$$ are $$$1, 3, 5, 15$$$, making the $$$4$$$-mersenne numbers only $$$1, 2$$$, and $$$4$$$, since $$$2^1 - 1 = 1$$$, $$$2^2 - 1 = 3$$$, and $$$2^4 - 1 = 15$$$, all of which are divisors of $$$15$$$.
In the third test case, we note that $$$2^6 - 1 = 63$$$, and the divisors of $$$63$$$ are $$$1, 3, 7, 9, 21, 63$$$, and of those, the $$$6$$$-mersenne numbers are only
