<p>Given a string <code>s</code>, consider all <em>duplicated substrings</em>: (contiguous) substrings of s that occur 2 or more times.&nbsp;The occurrences&nbsp;may overlap.</p>

<p>Return <strong>any</strong> duplicated&nbsp;substring that has the longest possible length.&nbsp;If <code>s</code> does not have a duplicated substring, the answer is <code>&quot;&quot;</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> s = "banana"
<strong>Output:</strong> "ana"
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> s = "abcd"
<strong>Output:</strong> ""
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= s.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution:
    def longestDupSubstring(self, s: str) -> str:
        def search(length: int) -> str:
            """ Search for a duplicate substring of given length using rolling hash. """
            h = 0
            base = 26
            mod = 2**63 - 1
            baseL = pow(base, length, mod)
            
            for i in range(length):
                h = (h * base + nums[i]) % mod
            
            seen = {h}
            for start in range(1, n - length + 1):
                # Rolling hash to update the hash value
                h = (h * base - nums[start-1] * baseL + nums[start + length - 1]) % mod
                if h in seen:
                    return s[start:start + length]
                seen.add(h)
            return ""
        
        nums = [ord(c) - ord('a') for c in s]
        n = len(s)
        
        left, right = 1, n
        result = ""
        
        while left <= right:
            mid = left + (right - left) // 2
            candidate = search(mid)
            if candidate:
                result = candidate
                left = mid + 1
            else:
                right = mid - 1
        
        return result

# Example usage:
# sol = Solution()
# print(sol.longestDupSubstring("banana"))  # Output: "ana"
# print(sol.longestDupSubstring("abcd"))    # Output: ""
21300