CF1983A Array Divisibility

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.

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.

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.