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46 lines
2.6 KiB
HTML
46 lines
2.6 KiB
HTML
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<p>You are given an integer <code>k</code> and an integer <code>x</code>.</p>
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<p>Consider <code>s</code> is the <strong>1-indexed </strong>binary representation of an integer <code>num</code>. The <strong>price</strong> of a number <code>num</code> is the number of <code>i</code>'s such that <code>i % x == 0</code> and <code><font face="monospace">s[i]</font></code> is a <strong>set bit</strong>.</p>
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<p>Return <em>the <b>greatest</b> integer </em><code>num</code><em> such that the sum of <strong>prices</strong> of all numbers from </em><code>1</code><em> to </em><code>num</code><em> is less than or equal to </em><code>k</code><em>.</em></p>
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<p><strong>Note</strong>:</p>
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<ul>
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<li>In the binary representation of a number <strong>set bit</strong> is a bit of value <code>1</code>.</li>
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<li>The binary representation of a number will be indexed from right to left. For example, if <code>s == 11100</code>, <code>s[4] == 1</code> and <code>s[2] == 0</code>.</li>
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</ul>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> k = 9, x = 1
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<strong>Output:</strong> 6
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<strong>Explanation:</strong> The numbers 1, 2, 3, 4, 5, and 6 can be written in binary representation as "1", "10", "11", "100", "101", and "110" respectively.
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Since x is equal to 1, the price of each number is the number of its set bits.
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The number of set bits in these numbers is 9. So the sum of the prices of the first 6 numbers is 9.
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So the answer is 6.</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> k = 7, x = 2
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<strong>Output:</strong> 9
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<strong>Explanation:</strong> Since x is equal to 2, we should just check even<sup>th</sup> bits.
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The second bit of binary representation of numbers 2 and 3 is a set bit. So the sum of their prices is 2.
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The second bit of binary representation of numbers 6 and 7 is a set bit. So the sum of their prices is 2.
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The fourth bit of binary representation of numbers 8 and 9 is a set bit but their second bit is not. So the sum of their prices is 2.
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Numbers 1, 4, and 5 don't have set bits in their even<sup>th</sup> bits in their binary representation. So the sum of their prices is 0.
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The second and the fourth bit of the binary representation of the number 10 are a set bit. So its price is 2.
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The sum of the prices of the first 9 numbers is 6.
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Because the sum of the prices of the first 10 numbers is 8, the answer is 9.</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>1 <= k <= 10<sup>15</sup></code></li>
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<li><code>1 <= x <= 8</code></li>
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</ul>
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