<p>For two strings <code>s</code> and <code>t</code>, we say &quot;<code>t</code> divides <code>s</code>&quot; if and only if <code>s = t + t + t + ... + t + t</code> (i.e., <code>t</code> is concatenated with itself one or more times).</p>

<p>Given two strings <code>str1</code> and <code>str2</code>, return <em>the largest string </em><code>x</code><em> such that </em><code>x</code><em> divides both </em><code>str1</code><em> and </em><code>str2</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> str1 = &quot;ABCABC&quot;, str2 = &quot;ABC&quot;
<strong>Output:</strong> &quot;ABC&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> str1 = &quot;ABABAB&quot;, str2 = &quot;ABAB&quot;
<strong>Output:</strong> &quot;AB&quot;
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> str1 = &quot;LEET&quot;, str2 = &quot;CODE&quot;
<strong>Output:</strong> &quot;&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= str1.length, str2.length &lt;= 1000</code></li>
	<li><code>str1</code> and <code>str2</code> consist of English uppercase letters.</li>
</ul>

class Solution {
public:
    bool isValidDiv(string& str1, string& str2) {
        const int s1 = str1.size(), s2 = str2.size(); // 6, 3
        if (s1 % s2 != 0) {
            return false;
        }

        for (int i = 0; i < s1; i += s2) {
            for (int j = i; j < i+s2; j++) {
                if (str1[j] != str2[j%s2]) {
                    return false; 
                }
            }
        }

        return true;
    }

    string gcdOfStrings(string str1, string str2) {
       if (str2.size() > str1.size()) { // ensure smaller string is s2
            str1.swap(str2);
       }

        int largest = str2.size();
        while (largest > 0) {
            string tmp = str2.substr(0, largest);
            if (isValidDiv(str1, tmp) && isValidDiv(str2, tmp)) {
                break;
            }

            largest--;
        } 

        return str2.substr(0, largest);
    }
};
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