Smallest Integer Divisible by K

class Solution:
    def smallestRepunitDivByK(self, k: int) -> int:
        #since multiples of 2(evens) and 5 have their multiples divisible bt 2 and 5. Thus they cannot have 11..11 as their multiple
        if k%2 == 0 or k%5 == 0:
            return -1

        res = 1
        '''GP A: 1 10 10^2 10^3...(r=10)
        N with i ones = sum of first i terms
        GP B: 1 10%K (10%K)^2 (10%K)^3...(r=10%k)
        (N with i ones)%k = (sum of first i terms)%k
        '''
        p, s, r = 1, 1, 10%k
        #upper bound is k; because since there are only k distinct remainders so at most after k iterations(each iteration means one more 1) the remainders would repeat.
        while s%k:
            res += 1
            p *= r #p is previous term in GP B(bi+1 = r*bi)
            s += p%k # sum of first res terms of GP B

        return res