You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Stack has an array $$$a$$$ of length $$$n$$$. He also has an empty set $$$S$$$. Note that $$$S$$$ is not a multiset.

He will do the following three-step operation exactly $$$n$$$ times:

1. Select an index $$$i$$$ such that $$$1 \leq i \leq |a|$$$.
2. Insert$$$^\dagger$$$ $$$a_i + i$$$ into $$$S$$$.
3. Delete $$$a_i$$$ from $$$a$$$. Note that the indices of all elements to the right of $$$a_i$$$ will decrease by $$$1$$$.

Note that after $$$n$$$ operations, $$$a$$$ will be empty.

Stack will now construct a new array $$$b$$$ which is $$$S$$$ sorted in decreasing order. Formally, $$$b$$$ is an array of size $$$|S|$$$ where $$$b_i$$$ is the $$$i$$$-th largest element of $$$S$$$ for all $$$1 \leq i \leq |S|$$$.

Find the lexicographically largest$$$^\ddagger$$$ $$$b$$$ that Stack can make.

$$$^\dagger$$$ A set can only contain unique elements. Inserting an element that is already present in a set will not change the elements of the set.

$$$^\ddagger$$$ An array $$$p$$$ is lexicographically larger than a sequence $$$q$$$ if and only if one of the following holds:

- $$$q$$$ is a prefix of $$$p$$$, but $$$p \ne q$$$; or
- in the first position where $$$p$$$ and $$$q$$$ differ, the array $$$p$$$ has a larger element than the corresponding element in $$$q$$$.

Note that $$$[3,1,4,1,5]$$$ is lexicographically larger than $$$[3,1,3]$$$, $$$[\,]$$$, and $$$[3,1,4,1]$$$ but not $$$[3,1,4,1,5,9]$$$, $$$[3,1,4,1,5]$$$, and $$$[4]$$$.

## Input Format
Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 3 \cdot 10^5$$$) — the length of array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_{n}$$$ ($$$1 \leq a_i \leq 10^9$$$) — the elements of array $$$a$$$.

The sum of $$$n$$$ over all test cases does not exceed $$$3 \cdot 10^5$$$.

## Output Format
For each test case, output the lexicographically largest $$$b$$$.

## Examples
```input
3
2
2 1
5
1 100 1000 1000000 1000000000
3
6 4 8
```
```output
3 2 
1000000005 1000004 1003 102 2 
11 7 6
```

## Note
In the first test case, select $$$i=1$$$ in the first operation, insert $$$a_1 + 1 = 3$$$ in $$$S$$$, and delete $$$a_1$$$ from $$$a$$$. After the first operation, $$$a$$$ becomes $$$a=[1]$$$. In the second operation, we select $$$i=1$$$ again and insert $$$a_1 + 1 = 2$$$ in $$$S$$$. Thus $$$S=\{2, 3\}$$$, and $$$b = [3, 2]$$$.

Note that if you select $$$i=2$$$ in the first operation, and $$$i=1$$$ in the second operation, $$$S=\{3\}$$$ as $$$3$$$ will be inserted twice, resulting in $$$b=[3]$$$.

As $$$[3,2]$$$ is lexicographically larger than $$$[3]$$$, we should select $$$i=1$$$ in the first operation.

In the second test case, in each operation, select the last element.

Now solve the problem and return the code.