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.

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 $a_i.$