Two lines

Given two strings S_1 and S_2, each consisting of lowercase Latin letters. For each string, a starting position (k_1 and k_2) is chosen. Beginning at this position, write out the characters of the string sequentially. After reaching the last character, return to the first character and continue writing characters in order. For example, if S_1 is $CAB$ and k_1 = 2 (with numbering starting from one), the resulting sequence is ABCABCABCABCABC\ldots. If S_2 is BCACAC and k_2 = 3, the sequence is ACACBACACBACAC\ldots. Thus, we obtain two infinite sequences of characters, denoted as T_1 and T_2.

For the given strings S_1 and S_2, find such k_1 and k_2 that the value of the following expression is maximized (where T_1[i] is the $i$-th character of T_1, and \operatorname{eq}(a, b) is $1$ if characters $a$ and $b$ are the same, or $0$ if they are different). In other words, you need to maximize the average number of matching characters in the resulting sequences.