B. ezraft and Array
time limit per test
1.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a single integer $$$n.$$$ Construct an array of $$$n$$$ distinct positive integers $$$a_1, \ldots, a_n$$$ such that for all $$$i \, (1 \le i \le n)$$$, $$$a_1 + a_2 + a_3 + \ldots + a_n$$$ is divisible by $$$a_i,$$$ or determine that no such array exists.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 50$$$). The description of the test cases follows.

The first and only line of each test case contains a single integer $$$n \, (1 \le n \le 50).$$$

Output

For each test case, if there is no solution, output a single integer $$$-1$$$.

Otherwise, output $$$n$$$ integers $$$a_1, \ldots, a_n \, (1 \le a_i \le 10^{17})$$$ — an array satisfying the conditions.

If there are multiple solutions, print any of them.

Example
Input
3
1
4
5
Output
1
1 9 2 6
12 3 10 20 15
Note

In the first test case, the condition is clearly satisfied, since $$$1$$$ is divisible by itself.

In the second test case, the output is $$$a = [1,9,2,6].$$$ We have $$$a_1 + a_2 + a_3 + a_4 = 18,$$$ which is divisible by all $$$a_i.$$$