For two strings s and t, we say that t divides s if and only if s can be formed by concatenating one or more copies of t together (i.e., s = t + t + ... + t).

Given two strings str1 and str2, return the largest string x such that x divides both str1 and str2. If no such string exists, return an empty string.

Constraints:

• $1 \leq$ str1.length, str2.length $\leq 1000$

• str1 and str2 consist of English uppercase letters.

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.