D. Range = √Sumtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an integer n. Find a sequence of n distinct integers a_1, a_2, \dots, a_n such that 1 \leq a_i \leq 10^9 for all i and \max(a_1, a_2, \dots, a_n) - \min(a_1, a_2, \dots, a_n)= \sqrt{a_1 + a_2 + \dots + a_n}.It can be proven that there exists a sequence of distinct integers that satisfies all the conditions above.InputThe first line of input contains t (1 \leq t \leq 10^4) — the number of test cases.The first and only line of each test case contains one integer n (2 \leq n \leq 3 \cdot 10^5) — the length of the sequence you have to find.The sum of n over all test cases does not exceed 3 \cdot 10^5.OutputFor each test case, output n space-separated distinct integers a_1, a_2, \dots, a_n satisfying the conditions in the statement. If there are several possible answers, you can output any of them. Please remember that your integers must be distinct!ExampleInput
3254Output
3 1
20 29 18 26 28
25 21 23 31
NoteIn the first test case, the maximum is 3, the minimum is 1, the sum is 4, and 3 - 1 = \sqrt{4}.In the second test case, the maximum is 29, the minimum is 18, the sum is 121, and 29-18 = \sqrt{121}.For each test case, the integers are all distinct.
3254
3 1 20 29 18 26 28 25 21 23 31 
['binary search', 'brute force', 'constructive algorithms', 'math', 'two pointers', '*1800']