codeforces#P1878B. Aleksa and Stack
Aleksa and Stack
Description
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 $i$ ($1\le i \le n-2$).
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.
Input
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 $2 \cdot 10^5$.
Output
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.
3
3
6
7
6 8 12
7 11 14 20 22 100
9 15 18 27 36 90 120
Note
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 $a_1+a_2$.