<p>You are given a string <code>s</code> of length <code>n</code>, and an integer <code>k</code>. You are tasked to find the <strong>longest subsequence repeated</strong> <code>k</code> times in string <code>s</code>.</p>

<p>A <strong>subsequence</strong> is a string that can be derived from another string by deleting some or no characters without changing the order of the remaining characters.</p>

<p>A subsequence <code>seq</code> is <strong>repeated</strong> <code>k</code> times in the string <code>s</code> if <code>seq * k</code> is a subsequence of <code>s</code>, where <code>seq * k</code> represents a string constructed by concatenating <code>seq</code> <code>k</code> times.</p>

<ul>
	<li>For example, <code>&quot;bba&quot;</code> is repeated <code>2</code> times in the string <code>&quot;bababcba&quot;</code>, because the string <code>&quot;bbabba&quot;</code>, constructed by concatenating <code>&quot;bba&quot;</code> <code>2</code> times, is a subsequence of the string <code>&quot;<strong><u>b</u></strong>a<strong><u>bab</u></strong>c<strong><u>ba</u></strong>&quot;</code>.</li>
</ul>

<p>Return <em>the <strong>longest subsequence repeated</strong> </em><code>k</code><em> times in string </em><code>s</code><em>. If multiple such subsequences are found, return the <strong>lexicographically largest</strong> one. If there is no such subsequence, return an <strong>empty</strong> string</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="example 1" src="https://assets.leetcode.com/uploads/2021/08/30/longest-subsequence-repeat-k-times.png" style="width: 457px; height: 99px;" />
<pre>
<strong>Input:</strong> s = &quot;letsleetcode&quot;, k = 2
<strong>Output:</strong> &quot;let&quot;
<strong>Explanation:</strong> There are two longest subsequences repeated 2 times: &quot;let&quot; and &quot;ete&quot;.
&quot;let&quot; is the lexicographically largest one.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;bb&quot;, k = 2
<strong>Output:</strong> &quot;b&quot;
<strong>Explanation:</strong> The longest subsequence repeated 2 times is &quot;b&quot;.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;ab&quot;, k = 2
<strong>Output:</strong> &quot;&quot;
<strong>Explanation:</strong> There is no subsequence repeated 2 times. Empty string is returned.
</pre>

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

<ul>
	<li><code>n == s.length</code></li>
	<li><code>2 &lt;= n, k &lt;= 2000</code></li>
	<li><code>2 &lt;= n &lt; k * 8</code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution:
    def longestSubsequenceRepeatedK(self, s: str, k: int) -> str:
        from collections import Counter, deque
        freq = Counter(s)
        chars = [c for c in freq if freq[c] >= k]
        if not chars:
            return ""
        res, queue = "", deque([""])
        while queue:
            seq = queue.popleft()
            for c in sorted(chars, reverse=True):
                new_seq = seq + c
                it, valid = iter(s), True
                for _ in range(k):
                    for ch in new_seq:
                        if ch not in it:
                            valid = False
                            break
                    if not valid:
                        break
                if valid:
                    if len(new_seq) > len(res) or (len(new_seq) == len(res) and new_seq > res):
                        res = new_seq
                    queue.append(new_seq)
        return res
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