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 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 the first challenge of the RGS Golfing Showdown. If you want to participate in the competition, you have 96 hours to submit your eligible answers. Remember there is 450 reputation in prizes! (See 6 of the rules)
Otherwise, this is still a regular code-golf challenge, so enjoy!