D. Abushogi's Revenge (Easy version)
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

This is the easy version of the problem. The difference between the versions is that in this version, you need to construct an initial game state that results in a draw.

Since MrMoon didn't mention abushogi in the editorial last time, he decided to take his revenge.

To settle the score, abushogi and void decided to play a game. There are $$$n$$$ wallets of Moons lined up on a table. The $$$i$$$-th wallet initially contains $$$a_i$$$ dollars ($$$a_i \ge 1$$$).

The game is played in turns, with abushogi taking the first turn (Turn 1), void taking Turn 2, and so on.

On a player's turn, they can repeatedly choose any non-empty wallet and take at least one dollar from it. A player's turn only ends immediately when the wallet they last took money from reaches exactly $$$0$$$ dollars.

Both players play optimally to maximize their own total amount of money.

Your task is to construct an array $$$a$$$ of $$$n$$$ integers ($$$1 \le a_i \le 10^9$$$) representing the initial amounts in the wallets such that if both players play optimally, the game ends in a draw (both players finish with the exact same amount of money).

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The only line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of wallets.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case:If it is impossible to end the game in a draw, output -1.

Otherwise, output $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the initial amounts of dollars in the wallets.

Example
Input
2
4
3
Output
1 1 1 1
-1