Regular Expression for Binary Numbers Divisible by n

Create a function that will return a regular expression string that is capable of evaluating binary strings (which consist of only 1s and 0s) and determining whether the given string represents a number divisible by n.

Tests

Inputs 1 <= n <= 18 will be tested

Each n will be tested against random invalid tests and random valid tests (which may or may not pass the regex test itself, accordingly).

Notes

• Strings that are not binary numbers should be rejected.
• Keep your solution under 5000 characters. This means you can't hard-code the answers.
• Only these characters may be included in your returned string:

  01?:*+^$()[]|

Javascript Notes

• Do not include the regex caps /.../. Your string will be used as such: RegExp(regexDivisibleBy(3)) in the tests.
• No funny business! There should be no need for prototyping, so don't even think about it.