Codeforces Round 873 (Div. 2) |
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Finished |

constructive algorithms

math

*800

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A. Divisible Array

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$n$$$.

Input

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 $$$a$$$.

Output

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.

Example

Input

71234567

Output

1 2 4 1 2 3 2 8 6 4 3 4 9 4 5 1 10 18 8 5 36 3 6 21 24 10 6 14

Note

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 $$$5$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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