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"title": "Sum of k-Mirror Numbers",
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"content": "<p>A <strong>k-mirror number</strong> is a <strong>positive</strong> integer <strong>without leading zeros</strong> that reads the same both forward and backward in base-10 <strong>as well as</strong> in base-k.</p>\n\n<ul>\n\t<li>For example, <code>9</code> is a 2-mirror number. The representation of <code>9</code> in base-10 and base-2 are <code>9</code> and <code>1001</code> respectively, which read the same both forward and backward.</li>\n\t<li>On the contrary, <code>4</code> is not a 2-mirror number. The representation of <code>4</code> in base-2 is <code>100</code>, which does not read the same both forward and backward.</li>\n</ul>\n\n<p>Given the base <code>k</code> and the number <code>n</code>, return <em>the <strong>sum</strong> of the</em> <code>n</code> <em><strong>smallest</strong> k-mirror numbers</em>.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> k = 2, n = 5\n<strong>Output:</strong> 25\n<strong>Explanation:\n</strong>The 5 smallest 2-mirror numbers and their representations in base-2 are listed as follows:\n base-10 base-2\n 1 1\n 3 11\n 5 101\n 7 111\n 9 1001\nTheir sum = 1 + 3 + 5 + 7 + 9 = 25. \n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> k = 3, n = 7\n<strong>Output:</strong> 499\n<strong>Explanation:\n</strong>The 7 smallest 3-mirror numbers are and their representations in base-3 are listed as follows:\n base-10 base-3\n 1 1\n 2 2\n 4 11\n 8 22\n 121 11111\n 151 12121\n 212 21212\nTheir sum = 1 + 2 + 4 + 8 + 121 + 151 + 212 = 499.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> k = 7, n = 17\n<strong>Output:</strong> 20379000\n<strong>Explanation:</strong> The 17 smallest 7-mirror numbers are:\n1, 2, 3, 4, 5, 6, 8, 121, 171, 242, 292, 16561, 65656, 2137312, 4602064, 6597956, 6958596\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 <= k <= 9</code></li>\n\t<li><code>1 <= n <= 30</code></li>\n</ul>\n",
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"code": "class Solution {\npublic:\n long long kMirror(int k, int n) {\n \n }\n};",
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"code": "class Solution {\n public long kMirror(int k, int n) {\n \n }\n}",
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"code": "class Solution(object):\n def kMirror(self, k, n):\n \"\"\"\n :type k: int\n :type n: int\n :rtype: int\n \"\"\"\n ",
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"code": "public class Solution {\n public long KMirror(int k, int n) {\n \n }\n}",
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"code": "/**\n * @param {number} k\n * @param {number} n\n * @return {number}\n */\nvar kMirror = function(k, n) {\n \n};",
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"code": "# @param {Integer} k\n# @param {Integer} n\n# @return {Integer}\ndef k_mirror(k, n)\n \nend",
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"code": "class Solution {\n func kMirror(_ k: Int, _ n: Int) -> Int {\n \n }\n}",
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"code": "func kMirror(k int, n int) int64 {\n \n}",
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"code": "class Solution {\n fun kMirror(k: Int, n: Int): Long {\n \n }\n}",
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"code": "impl Solution {\n pub fn k_mirror(k: i32, n: i32) -> i64 {\n \n }\n}",
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"code": "class Solution {\n\n /**\n * @param Integer $k\n * @param Integer $n\n * @return Integer\n */\n function kMirror($k, $n) {\n \n }\n}",
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"code": "function kMirror(k: number, n: number): number {\n\n};",
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"code": "(define/contract (k-mirror k n)\n (-> exact-integer? exact-integer? exact-integer?)\n\n )",
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"code": "defmodule Solution do\n @spec k_mirror(k :: integer, n :: integer) :: integer\n def k_mirror(k, n) do\n\n end\nend",
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"hints": [
"Since we need to reduce search space, instead of checking if every number is a palindrome in base-10, can we try to \"generate\" the palindromic numbers?",
"If you are provided with a d digit number, how can you generate a palindrome with 2*d or 2*d - 1 digit?",
"Try brute-forcing and checking if the palindrome you generated is a \"k-Mirror\" number."
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