Beautiful Primes

John Nash is a talented mathematician at Princeton. Due to
his prolific contributions in academia, he was even recruited
to the Pentagon at a young age to crack enemy encrypted
telecommunication. In his first task, John was able to decipher
the code mentally, much to the astonishment of other
decrypters. In his everyday life, he is constantly looking for
patterns in magazines to newspapers to keep his senses
sharp.

Recently, he has been cracking away at a cryptography
problem that involves prime numbers. Given a positive integer
$N$, the puzzle needs him
to produce a “beautiful" list of $N$ primes. A list of $N$ primes numbers is considered
beautiful if each prime is at most $1\, 000\, 000$, and their product has
exactly $N$
digits.

For example, if $N =
1$, then the list $[5]$ is beautiful because its length
is $1$, and its product
$5$ has $1$ digit.

For $N = 2$, the list
$[3, 7]$ is beautiful
because its product $3 \times 7 =
21$ has the required digit count of $2$.

For $N = 3$, the list
$[5, 5, 7]$ is beautiful
because its product $5 \times 5
\times 7 = 175$ has the required digit count of
$3$.

John wants to practice his mental math and impress his colleagues. He needs you to write a program that helps him practice this interesting task. John Nash has a beautiful mind, so won’t you help him find some beautiful primes?

The first line of input consists of a single integer
$T$ ($1 \leq T \leq 50$), the number of
test cases.

$T$ lines follow, each of
which is a test case consisting of a single integer
$N$ ($1 \leq N \leq 1\, 000$).

For each test case, print, on a separate line, a list of
$N$ space-delimited
beautiful primes that are each no greater than $1\, 000\, 000$. The primes do not
have to be distinct, and may be printed in any order. If there
are multiple answers, you may print any of them.

Sample Input 1 | Sample Output 1 |
---|---|

3 1 2 3 |
5 3 7 5 5 7 |