Read problem statements in [Mandarin], [Russian], and [Vietnamese] as well.

You are given a positive integer N. You have to print exactly N + 1 positive integers
satisfying the following conditions:

Exactly one value should appear twice, all the remaining values should appear only once.
Sum of all these values should be equal to 2^{N}.

You have to print the values in non-decreasing order. If there are multiple solutions, you can print any of them.

------ Input Format ------

• The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
• The first and only line of each test case contains a single integer N.

------ Output Format ------

For each test case, print a single line containing N + 1 positive integers in non-decreasing order that satisfy the given conditions. If there are multiple solutions, you may print any of them.

------ Constraints ------

$1 ≤T ≤60$
$1 ≤N ≤60$

------ subtasks ------

Subtask 1 (100 points): Original constraints

----- Sample Input 1 ------
2
3
4

----- Sample Output 1 ------
1 2 2 3
1 2 3 3 7
----- explanation 1 ------
Test Case $1$: $2$ is repeated twice and the remaining elements occurred only once and the sum of all the elements is equal to $8$, which is $2^{3}$.

Test Case $2$: $3$ is repeated twice and the remaining elements occurred only once and the sum of all the elements is equal to $16$, which is $2^{4}$.

见题面

见题面