A. Divisible Array
constructive algorithms; math
You are given a positive integer \(n\). Please find an array \(a_1, a_2, \ldots, a_n\) that is perfect.A perfect array \(a_1, a_2, \ldots, a_n\) satisfies the following criteria: \(1 \le a_i \le 1000\) for all \(1 \le i \le n\). \(a_i\) is divisible by \(i\) for all \(1 \le i \le n\). \(a_1 + a_2 + \ldots + a_n\) is divisible by \(n\).
Each test contains multiple test cases. The first line contains the number of test cases \(t\) (\(1 \le t \le 200\)). The description of the test cases follows.The only line of each test case contains a single positive integer \(n\) (\(1 \le n \le 200\)) — the length of the array \(a\).
For each test case, output an array \(a_1, a_2, \ldots, a_n\) that is perfect.We can show that an answer always exists. If there are multiple solutions, print any.
In the third test case: \(a_1 = 1\) is divisible by \(1\). \(a_2 = 2\) is divisible by \(2\). \(a_3 = 3\) is divisible by \(3\). \(a_1 + a_2 + a_3 = 1 + 2 + 3 = 6\) is divisible by \(3\). In the fifth test case: \(a_1 = 3\) is divisible by \(1\). \(a_2 = 4\) is divisible by \(2\). \(a_3 = 9\) is divisible by \(3\). \(a_4 = 4\) is divisible by \(4\). \(a_5 = 5\) is divisible by \(5\). \(a_1 + a_2 + a_3 + a_4 + a_5 = 3 + 4 + 9 + 4 + 5 = 25\) is divisible by \(5\).