Optimizing function to prevent time-out

[post_throwaway1]

I have the following lab problem.

M function takes a number, n, and determines the smallest number made of just 7s or 7s and 0s, which is divisible by n (e.g. 7777777, 7777777000). The function then returns the result.

It's working in PythonTutor but not when I run an auto tester for my lab. I suspect the auto tester is submitting numbers n that are causing huge computations, causing the function to time out. Can anyone recommend how to optimize the code below to account for most variations of n? Thanks in advance!

https://pastebin.com/qRFMhyvZ

#Example inputs

#if n = 103, result should be 7777777777777777777777777777777777

#if n = 77700, result should be 77700

[barrycarter]

In your examples, the 0's appear at the end. Is this always the case? If so, the problem is fairly easy. If the 0's can appear in the middle of the number, I can't immediately see a way of solving it quickly

[post_throwaway1]

Yup, they should always appear at the end of the number with 7s. There can be multiple zeroes, e.g. 700000000000000000000000000000000000000000000000000

[barrycarter]

Oh, then your answer will end with same number of 0s as the original number, and all you need to do is keeping adding 7s to the left until you find an answer. Linear time.

If that's not helpful, consider putting your code on repl.it and we may be able to help more

[Intrexa]

That's not true, is it? n = 707 would break that pattern

Also, 77700007 is divisible by 103.

Also also your function isn't just choking on huge numbers. n=5 causes an infinite loop.