<p>Given an integer array <code>queries</code> and a <strong>positive</strong> integer <code>intLength</code>, return <em>an array</em> <code>answer</code> <em>where</em> <code>answer[i]</code> <em>is either the </em><code>queries[i]<sup>th</sup></code> <em>smallest <strong>positive palindrome</strong> of length</em> <code>intLength</code> <em>or</em> <code>-1</code><em> if no such palindrome exists</em>.</p>

<p>A <strong>palindrome</strong> is a number that reads the same backwards and forwards. Palindromes cannot have leading zeros.</p>

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

<pre>
<strong>Input:</strong> queries = [1,2,3,4,5,90], intLength = 3
<strong>Output:</strong> [101,111,121,131,141,999]
<strong>Explanation:</strong>
The first few palindromes of length 3 are:
101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, ...
The 90<sup>th</sup> palindrome of length 3 is 999.
</pre>

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

<pre>
<strong>Input:</strong> queries = [2,4,6], intLength = 4
<strong>Output:</strong> [1111,1331,1551]
<strong>Explanation:</strong>
The first six palindromes of length 4 are:
1001, 1111, 1221, 1331, 1441, and 1551.
</pre>

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

<ul>
	<li><code>1 &lt;= queries.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= queries[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= intLength&nbsp;&lt;= 15</code></li>
</ul>

import math
class Solution:
    
    def kthPalindrome(self, queries: List[int], intLength: int) -> List[int]:
        # if queries[i] > 9 * 10^ceil((intLength - 2) / 2), then answer[i] = -1

        maxK = 9 * int(math.pow(10, int(math.ceil((intLength - 2) / 2))))
        def helper(query: int) -> int:
            if query > maxK:
                return -1
            
            if intLength == 1:
                return query
            
            if intLength == 2:
                return query + 10 * query
            
            innerPalLimit = int(math.pow(10, int(math.ceil((intLength - 2) / 2))))
            divResult = (query - 1) // innerPalLimit
            modResult = (query - 1) % innerPalLimit

            outerPart = (divResult + 1) * math.pow(10, intLength - 1) + (divResult + 1)
            innerPart = helperZerosAllowed(modResult, intLength - 2) * 10

            return int(outerPart + innerPart)
        
        # allows 0s in the outer part of the palindrome and allow query to be 0
        def helperZerosAllowed(query: int, intLength: int) -> int:
            if intLength == 1:
                return query
            
            if intLength == 2:
                return query + 10 * query

            # take query and flipped version of query. merge to form palindrome
            if intLength % 2 == 0:
                temp = str(query) + str(query)[::-1]
            else:
                temp = str(query) + (str(query)[::-1])[1:]
            
            if len(temp) < intLength:
                return int(temp) * int(math.pow(10, (intLength - len(temp)) / 2))
            return int(temp)

        return [helper(q) for q in queries]
        #return [helperZerosAllowed(q, intLength) for q in queries]
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