<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:
        mods = [[0]*10 for _ in range(n)]
        res = [None]*n
        for i in range(n-1,-1,-1):
            for j in range(10):
                if i == n -1:
                    mods[i][j] = j % k
                else:
                     mods[i][j] = (mods[i+1][j]*10) % k
        @lru_cache(None)
        def dfs(i,cur):
            if i == (n+1)//2:
                if cur%k == 0:
                    return True
                else:
                    return False
            cur_mod = 0
            digit_pos = set([i, n - i - 1])
            for j in range(9,-1,-1):
                cur_mod = mods[i][j]
                another = mods[n-1-i][j]
                for pos in digit_pos:
                    res[pos] = str(j)
                if n%2 and i == n//2:
                    r = dfs(i+1,(cur + cur_mod)%k)
                    if r:return True
                else:
                    r = dfs(i+1,(cur + cur_mod + another)%k)
                    if r:return True
            return False
        dfs(0,0)
        return "".join(res)
173861