codeforces#P1983A. Array Divisibility
Array Divisibility
Description
An array of integers $a_1,a_2,\cdots,a_n$ is beautiful subject to an integer $k$ if it satisfies the following:
- The sum of $a_{j}$ over all $j$ such that $j$ is a multiple of $k$ and $1 \le j \le n $, itself, is a multiple of $k$.
- More formally, if $\sum_{k | j} a_{j}$ is divisible by $k$ for all $1 \le j \le n$ then the array $a$ is beautiful subject to $k$. Here, the notation ${k|j}$ means $k$ divides $j$, that is, $j$ is a multiple of $k$.
It can be shown that an answer always exists.
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). The description of the test cases follows.
The first and only line of each test case contains a single integer $n$ ($1 \le n \le 100$) — the size of the array.
For each test case, print the required array as described in the problem statement.
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). The description of the test cases follows.
The first and only line of each test case contains a single integer $n$ ($1 \le n \le 100$) — the size of the array.
Output
For each test case, print the required array as described in the problem statement.
3
3
6
7
4 22 18
10 6 15 32 125 54
23 18 27 36 5 66 7
Note
In the second test case, when $n = 6$, for all integers $k$ such that $1 \le k \le 6$, let $S$ be the set of all indices of the array that are divisible by $k$.
- When $k = 1$, $S = \{1, 2, 3,4,5,6\}$ meaning $a_1+a_2+a_3+a_4+a_5+a_6=242$ must be divisible by $1$.
- When $k = 2$, $S = \{2,4,6\}$ meaning $a_2+a_4+a_6=92$ must be divisible by $2$.
- When $k = 3$, $S = \{3,6\}$ meaning $a_3+a_6=69$ must divisible by $3$.
- When $k = 4$, $S = \{4\}$ meaning $a_4=32$ must divisible by $4$.
- When $k = 5$, $S = \{5\}$ meaning $a_5=125$ must divisible by $5$.
- When $k = 6$, $S = \{6\}$ meaning $a_6=54$ must divisible by $6$.