Define S = [s,n] as the string S which consists of n connected strings s. For example, ["abc", 3] ="abcabcabc". 
On the other hand, we define that string s1 can be obtained from string s2 if we can remove some characters from s2 such that it becomes s1. For example, “abc”  can be obtained from “abdbec” based on our definition, but it can not be obtained from “acbbe”.
You are given two non-empty strings s1 and s2 (each at most 100 characters long) and two integers 0 ≤ n1 ≤ 106 and 1 ≤ n2 ≤ 106. Now consider the strings S1 and S2, where S1=[s1,n1] and S2=[s2,n2]. Find the maximum integer M such that [S2,M] can be obtained from S1.
Example:
Input:
s1="acb", n1=4
s2="ab", n2=2
Return:
2
class Solution:
     def getMaxRepetitions(self, s1, n1, s2, n2):
         start = {} # s2_idx : s1_round, s2_round
         s1_round, s2_round, s2_idx = 0, 0, 0
         while s1_round < n1:
             s1_round += 1
             for ch in s1:
                 if ch == s2[s2_idx]:
                     s2_idx += 1
                     if s2_idx == len(s2):
                         s2_round += 1
                         s2_idx = 0
             if s2_idx in start:
                 prev_s1_round, prev_s2_round = start[s2_idx]
                 circle_s1_round, circle_s2_round = s1_round - prev_s1_round, s2_round - prev_s2_round
                 res = (n1 - prev_s1_round) // circle_s1_round * circle_s2_round
                 left_s1_round = (n1 - prev_s1_round) % circle_s1_round + prev_s1_round
                 for key, val in start.items():
                     if val[0] == left_s1_round:
                         res += val[1]
                         break
                 return res // n2
             else:
                 start[s2_idx] = (s1_round, s2_round)
         return s2_round // n2
class Solution:
     def getMaxRepetitions(self, s1, n1, s2, n2):
         start = {} # s2_idx : s1_round, s2_round
         s1_round, s2_round, s2_idx = 0, 0, 0
         while s1_round < n1:
             s1_round += 1
             for ch in s1:
                 if ch == s2[s2_idx]:
                     s2_idx += 1
                     if s2_idx == len(s2):
                         s2_round += 1
                         s2_idx = 0
             if s2_idx in start:
                 prev_s1_round, prev_s2_round = start[s2_idx]
                 circle_s1_round, circle_s2_round = s1_round - prev_s1_round, s2_round - prev_s2_round
                 res = (n1 - prev_s1_round) // circle_s1_round * circle_s2_round
                 left_s1_round = (n1 - prev_s1_round) % circle_s1_round + prev_s1_round
                 for key, val in start.items():
                     if val[0] == left_s1_round:
                         res += val[1]
                         break
                 return res // n2
             else:
                 start[s2_idx] = (s1_round, s2_round)
         return s2_round // n2