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61 lines
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61 lines
2.0 KiB
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<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>
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<ul>
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<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>
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<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>
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</ul>
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<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>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> k = 2, n = 5
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<strong>Output:</strong> 25
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<strong>Explanation:
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</strong>The 5 smallest 2-mirror numbers and their representations in base-2 are listed as follows:
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base-10 base-2
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1 1
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3 11
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5 101
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7 111
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9 1001
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Their sum = 1 + 3 + 5 + 7 + 9 = 25.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> k = 3, n = 7
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<strong>Output:</strong> 499
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<strong>Explanation:
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</strong>The 7 smallest 3-mirror numbers are and their representations in base-3 are listed as follows:
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base-10 base-3
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1 1
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2 2
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4 11
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8 22
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121 11111
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151 12121
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212 21212
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Their sum = 1 + 2 + 4 + 8 + 121 + 151 + 212 = 499.
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> k = 7, n = 17
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<strong>Output:</strong> 20379000
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<strong>Explanation:</strong> The 17 smallest 7-mirror numbers are:
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1, 2, 3, 4, 5, 6, 8, 121, 171, 242, 292, 16561, 65656, 2137312, 4602064, 6597956, 6958596
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>2 <= k <= 9</code></li>
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<li><code>1 <= n <= 30</code></li>
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</ul>
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