A16203. 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 $a_1+a_2$ .