<p>You are given two <strong>positive</strong> integers <code>n</code> and <code>k</code>.</p>

<p>An integer <code>x</code> is called <strong>k-palindromic</strong> if:</p>

<ul>
	<li><code>x</code> is a <span data-keyword="palindrome-integer">palindrome</span>.</li>
	<li><code>x</code> is divisible by <code>k</code>.</li>
</ul>

<p>Return the<strong> largest</strong> integer having <code>n</code> digits (as a string) that is <strong>k-palindromic</strong>.</p>

<p><strong>Note</strong> that the integer must <strong>not</strong> have leading zeros.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 3, k = 5</span></p>

<p><strong>Output:</strong> <span class="example-io">&quot;595&quot;</span></p>

<p><strong>Explanation:</strong></p>

<p>595 is the largest k-palindromic integer with 3 digits.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 1, k = 4</span></p>

<p><strong>Output:</strong> <span class="example-io">&quot;8&quot;</span></p>

<p><strong>Explanation:</strong></p>

<p>4 and 8 are the only k-palindromic integers with 1 digit.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 5, k = 6</span></p>

<p><strong>Output:</strong> <span class="example-io">&quot;89898&quot;</span></p>
</div>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= k &lt;= 9</code></li>
</ul>

class Solution:
  def largestPalindrome(self, n: int, k: int) -> str:
    ret = [None] * n
    visited = set()
    m = (n + 1) // 2

    pow10 = [1] * n
    for i in range(1, n):
      pow10[i] = pow10[i - 1] * 10 % k

    def dfs(level, modval):
      #print(level, modval)
      if level == m:
        return modval == 0
      visited.add((level, modval))
      for i in range(9, -1, -1):
        if n % 2 == 1 and level == m - 1:
          newmodval = (modval + i * pow10[level]) % k
        else:
          newmodval = (modval + i * pow10[level] + i * pow10[n - 1 - level]) % k
        
        if (level + 1, newmodval) not in visited and dfs(level + 1, newmodval):
          ret[level] = ret[n - 1 - level] = str(i) 
          return True
       
      return False 
    
    dfs(0, 0)
    return ''.join(ret)
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