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A _binary multiple_ of a positive integer `k` is a positive integer `n` such that `n` is written only with `0`s and `1`s in base 10 and `n` is a multiple of `k`. For example, `111111` is a _binary multiple_ of 3.
It is easy to show that a positive integer has infinitely many _binary multiples_. See [here][blog] for a construction proof of one _binary multiple_ for each `k`. Multiplying by powers of `10` you get infinitely many more.
# Your task
Given a positive integer `k`, return the smallest binary multiple of `k`.
# Input
A positive integer `k`.
# Output
A positive integer `n`, the smallest binary multiple of `k`.
# Test cases
```
2 -> 10
3 -> 111
4 -> 100
5 -> 10
6 -> 1110
7 -> 1001
8 -> 1000
9 -> 111111111
10 -> 10
11 -> 11
12 -> 11100
13 -> 1001
14 -> 10010
15 -> 1110
16 -> 10000
17 -> 11101
18 -> 1111111110
19 -> 11001
20 -> 100
100 -> 100
```
This is Code Golf so shortest submission in bytes, wins! If you liked this challenge, consider upvoting it... And happy golfing!
This is a regular code-golf challenge, so enjoy!
[blog]: https://mathspp.com/blog/binary-multiples