C. Training Before the Olympiad
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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

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 $$$a$$$.

Example
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 $$$24$$$.