CF2246B ezraft and Array

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.

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). $

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.

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. $