"""
For two strings s and t, we say "t divides s" if and only if s = t + ... + t (i.e., t is concatenated with itself one or more times).
Given two strings str1 and str2, return the largest string x such that x divides both str1 and str2.

Example 1:
Input: str1 = "ABCABC", str2 = "ABC"
Output: "ABC"

Example 2:
Input: str1 = "ABABAB", str2 = "ABAB"
Output: "AB"

Example 3:
Input: str1 = "LEET", str2 = "CODE"
Output: ""

Constraints:
1 <= str1.length, str2.length <= 1000
str1 and str2 consist of English uppercase letters.

analysis:
math
TC: O(M + N)
"""
from math import gcd


class GreatestCommonDivisorOfStrings:
    def gcdOfStrings(self, str1: str, str2: str) -> str:
        if str1 + str2 != str2 + str1:
            return ""

        max_length = gcd(len(str1), len(str2))
        return str1[:max_length]
