Codeforces Round 836 (Div. 2) |
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You 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 $$$$$$\max(a_1, a_2, \dots, a_n) - \min(a_1, a_2, \dots, a_n)= \sqrt{a_1 + a_2 + \dots + a_n}.$$$$$$
It can be proven that there exists a sequence of distinct integers that satisfies all the conditions above.
The first line of input contains $$$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$$$.
For each test case, output $$$n$$$ space-separated distinct integers $$$a_1, a_2, \dots, a_n$$$ satisfying the conditions in the statement.
If there are several possible answers, you can output any of them. Please remember that your integers must be distinct!
3254
3 1 20 29 18 26 28 25 21 23 31
In the first test case, the maximum is $$$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.
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