Description

Little $\zeta$ loves non-negative integer powers of $2$.

He asks you to construct an integer sequence that satisfies the following conditions:

• Its length is a non-negative integer power of $2$.
• Its elements are all non-negative integer powers of $2$.
• The sum of its elements is $m$.

That's still too easy. Therefore, you are asked to minimize the length of the sequence, and based on this, minimize the lexicographic order of the sequence.

It can be proven that a proper solution always exists under the given constraints.

Input Format

The first line of input contains a single integer $T$, denoting the number of test cases. The description of test cases follows.

The first and only line of each test case contains a single integer $m$.

Output Format

For each test case, output a single line containing a series of numbers, separated by space, as your constructed sequence. It is guaranteed the sum of the lengths of the answer sequences of each test case does not exceed $2\times10^6$.

2
5
6

1 4
2 4

Hint

Sample Explanation

$1, 2, 4$ are all non-negative integer powers of $2$.

The sequence $[1, 4]$ contains all non-negative integer powers of $2$, has a sum of $1 + 4 = 5 = m$, and has a length of $2$, also a non-negative integer power of $2$.

It can be proven that there is no sequence of strict shorter length nor smaller lexicographic order, hence the answer is sequence $[1, 4]$. So is the case for $m = 6$.

Constraints

For all tests, it's guaranteed that $1 \leq T \leq 10^4$, $1 \leq m \leq 10^{18}$ and the sum of the lengths of the answer sequences of each test case does not exceed $2\times10^6$. Each test is worth $10$ points.