CF1878B Aleksa and Stack

After the Serbian Informatics Olympiad, Aleksa was very sad, because he didn't win a medal (he didn't know stack), so Vasilije came to give him an easy problem, just to make his day better. Vasilije gave Aleksa a positive integer $ n $ ( $ n \ge 3 $ ) and asked him to construct a strictly increasing array of size $ n $ of positive integers, such that - $ 3\cdot a_{i+2} $ is not divisible by $ a_i+a_{i+1} $ for each $ i $ ( $ 1\le i \le n-2 $ ). Note that a strictly increasing array $ a $ of size $ n $ is an array where $ a_i < a_{i+1} $ for each $ i $ ( $ 1 \le i \le n-1 $ ).Since Aleksa thinks he is a bad programmer now, he asked you to help him find such an array.

Each test consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The description of test cases follows. The first line of each test case contains a single integer $ n $ ( $ 3 \le n \le 2 \cdot 10^5 $ ) — the number of elements in array. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output $ n $ integers $ a_1, a_2, a_3, \dots, a_n $ ( $ 1 \le a_i \le 10^9 $ ). It can be proved that the solution exists for any $ n $ . If there are multiple solutions, output any of them.

In the first test case, $ a_1=6 $ , $ a_2=8 $ , $ a_3=12 $ , so $ a_1+a_2=14 $ and $ 3 \cdot a_3=36 $ , so $ 3 \cdot a_3 $ is not divisible by $ a_1+a_2 $ .