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 c++17.

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:
```cpp
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Masha and Olya have an important team olympiad coming up soon. In honor of this, Masha, for warm-up, suggested playing a game with Olya:

There is an array $$$a$$$ of size $$$n$$$. Masha goes first, and the players take turns. Each move is described by the following sequence of actions:

$$$\bullet$$$ If the size of the array is $$$1$$$, the game ends.

$$$\bullet$$$ The player who is currently playing chooses two different indices $$$i$$$, $$$j$$$ ($$$1 \le i, j \le |a|$$$), and performs the following operation — removes $$$a_i$$$ and $$$a_j$$$ from the array and adds to the array a number equal to $$$\lfloor \frac{a_i + a_j}{2} \rfloor \cdot 2$$$. In other words, first divides the sum of the numbers $$$a_i$$$, $$$a_j$$$ by $$$2$$$ rounding down, and then multiplies the result by $$$2$$$.

Masha aims to maximize the final number, while Olya aims to minimize it.

Masha and Olya decided to play on each non-empty prefix of the initial array $$$a$$$, and asked for your help.

For each $$$k = 1, 2, \ldots, n$$$, answer the following question. Let only the first $$$k$$$ elements of the array $$$a$$$ be present in the game, with indices $$$1, 2, \ldots, k$$$ respectively. What number will remain at the end with optimal play by both players?

## Input Format
The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.

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

The second line contains $$$n$$$ integers $$$a_1,a_2, \ldots,a_n$$$ ($$$1 \leq a_i \leq 10^9$$$) — the array on which Masha and Olya play.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

## Output Format
For each test case, output $$$n$$$ integers. The $$$k$$$-th of these numbers should be equal to the number that will remain at the end with optimal play by both players, on the array consisting of the first $$$k$$$ elements of the array $$$a$$$.

## Examples
```input
4
1
31
6
6 3 7 2 5 4
3
3 10 11
5
7 13 11 19 1
```
```output
31 
6 8 16 18 22 26 
3 12 24 
7 20 30 48 50
```

## Note
In the third test case, for a prefix of length $$$1$$$, the answer is $$$3$$$. For a prefix of length $$$2$$$, Masha has only one move, so the answer is $$$12$$$. For a prefix of length $$$3$$$, Masha has three possible moves: she chooses $$$3$$$ and $$$10$$$, then the final number is $$$22$$$, $$$3$$$ and $$$11$$$, then the final number is $$$24$$$, $$$10$$$ and $$$11$$$, then the final number is $$$22$$$, so Masha will choose $$$3$$$ and $$$11$$$ and get $$$24$$$.

Now solve the problem and return the code.