Codeforces Round 900 (Div. 3) |
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Finished |

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constructive algorithms

math

*800

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B. Aleksa and Stack

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAfter the Serbian Informatics Olympiad, Aleksa was very sad, because he didn't win a medal (he didn't know stack), so Vasilije came to give him an easy problem, just to make his day better.

Vasilije gave Aleksa a positive integer $$$n$$$ ($$$n \ge 3$$$) and asked him to construct a strictly increasing array of size $$$n$$$ of positive integers, such that

- $$$3\cdot a_{i+2}$$$ is not divisible by $$$a_i+a_{i+1}$$$ for each $$$i$$$ ($$$1\le i \le n-2$$$).

Since Aleksa thinks he is a bad programmer now, he asked you to help him find such an array.

Input

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$3 \le n \le 2 \cdot 10^5$$$) — the number of elements in array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output $$$n$$$ integers $$$a_1, a_2, a_3, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$).

It can be proved that the solution exists for any $$$n$$$. If there are multiple solutions, output any of them.

Example

Input

3367

Output

6 8 12 7 11 14 20 22 100 9 15 18 27 36 90 120

Note

In the first test case, $$$a_1=6$$$, $$$a_2=8$$$, $$$a_3=12$$$, so $$$a_1+a_2=14$$$ and $$$3 \cdot a_3=36$$$, so $$$3 \cdot a_3$$$ is not divisible by $$$a_1+a_2$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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