A. Array Divisibility
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$k$$$.
Given $$$n$$$, find an array of positive nonzero integers, with each element less than or equal to $$$10^5$$$ that is beautiful subject to all $$$1 \le k \le n$$$.

It can be shown that an answer always exists.

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.

Example
Input
3
3
6
7
Output
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 $$$6$$$.
The array $$$a = [10, 6, 15, 32, 125, 54]$$$ satisfies all of the above conditions. Hence, $$$a$$$ is a valid array.