A. Find Array
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Given $$$n$$$, find any array $$$a_1, a_2, \ldots, a_n$$$ of integers such that all of the following conditions hold:

  • $$$1 \le a_i \le 10^9$$$ for every $$$i$$$ from $$$1$$$ to $$$n$$$.

  • $$$a_1 < a_2 < \ldots <a_n$$$

  • For every $$$i$$$ from $$$2$$$ to $$$n$$$, $$$a_i$$$ isn't divisible by $$$a_{i-1}$$$

It can be shown that such an array always exists under the constraints of the problem.

Input

The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). Description of the test cases follows.

The only line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 1000$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^4$$$.

Output

For each test case print $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ — the array you found. If there are multiple arrays satisfying all the conditions, print any of them.

Example
Input
3
1
2
7
Output
1
2 3
111 1111 11111 111111 1111111 11111111 111111111
Note

In the first test case, array $$$[1]$$$ satisfies all the conditions.

In the second test case, array $$$[2, 3]$$$ satisfies all the conditions, as $$$2<3$$$ and $$$3$$$ is not divisible by $$$2$$$.

In the third test case, array $$$[111, 1111, 11111, 111111, 1111111, 11111111, 111111111]$$$ satisfies all the conditions, as it's increasing and $$$a_i$$$ isn't divisible by $$$a_{i-1}$$$ for any $$$i$$$ from $$$2$$$ to $$$7$$$.