D. Range = √Sum
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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 $$$3 \cdot 10^5$$$.

Output

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!

Example
Input
3
2
5
4
Output
3 1
20 29 18 26 28
25 21 23 31
Note

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.