Juggler Sequence is a series of integer number in which the first term starts with a positive integer number *a* and the remaining terms are generated from the immediate previous term using the below recurrence relation:

Given a number *N* your task is to print the space separated Juggler Sequence for this number as the first term of the sequence.

Examples:

```
Input: 9
Output: 9, 27, 140, 11, 36, 6, 2, 1
We start with 9 and use above formula to get
next terms.
Input: 6
Output: 6, 2, 1
```

**Input:**

The first line of input contains an integer T denoting the no of test cases. Then T test cases follow. Each line contains an integer N.

**Output:**

For each test case in a new line print the space separated juggler sequence for number N as the first term of the sequence.

**Constraints:**

1<=T<=100

1<=N<=100

**Example:
Input:**

2

9

6

9 27 140 11 36 6 2 1

6 2 1

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