Code Golf
liek
A _binary multiple_ of a positive integer k is a positive integer n such that n is written only with 0s and 1s 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.

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

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