leetcode-problemset/leetcode-cn/originData/maximum-number-that-sum-of-the-prices-is-less-than-or-equal-to-k.json

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            "title": "Maximum Number That Sum of the Prices Is Less Than or Equal to K",
            "titleSlug": "maximum-number-that-sum-of-the-prices-is-less-than-or-equal-to-k",
            "content": "<p>You are given an integer <code>k</code> and an integer <code>x</code>.</p>\n\n<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>&#39;s such that <code>i % x == 0</code> and <code><font face=\"monospace\">s[i]</font></code> is a <strong>set bit</strong>.</p>\n\n<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>\n\n<p><strong>Note</strong>:</p>\n\n<ul>\n\t<li>In the binary representation of a number <strong>set bit</strong> is a bit of value <code>1</code>.</li>\n\t<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>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> k = 9, x = 1\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> The numbers 1, 2, 3, 4, 5, and 6 can be written in binary representation as &quot;1&quot;, &quot;10&quot;, &quot;11&quot;, &quot;100&quot;, &quot;101&quot;, and &quot;110&quot; respectively.\nSince x is equal to 1, the price of each number is the number of its set bits.\nThe number of set bits in these numbers is 9. So the sum of the prices of the first 6 numbers is 9.\nSo the answer is 6.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> k = 7, x = 2\n<strong>Output:</strong> 9\n<strong>Explanation:</strong> Since x is equal to 2, we should just check even<sup>th</sup> bits.\nThe second bit of binary representation of numbers 2 and 3 is a set bit. So the sum of their prices is 2.\nThe second bit of binary representation of numbers 6 and 7 is a set bit. So the sum of their prices is 2.\nThe 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.\nNumbers 1, 4, and 5 don&#39;t have set bits in their even<sup>th</sup> bits in their binary representation. So the sum of their prices is 0.\nThe second and the fourth bit of the binary representation of the number 10 are a set bit. So its price is 2.\nThe sum of the prices of the first 9 numbers is 6.\nBecause the sum of the prices of the first 10 numbers is 8, the answer is 9.</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k &lt;= 10<sup>15</sup></code></li>\n\t<li><code>1 &lt;= x &lt;= 8</code></li>\n</ul>\n",
            "translatedTitle": "价值和小于等于 K 的最大数字",
            "translatedContent": "<p>给你一个整数&nbsp;<code>k</code>&nbsp;和一个整数&nbsp;<code>x</code>&nbsp;。</p>\n\n<p>令 <code>s</code>&nbsp;为整数&nbsp;<code>num</code>&nbsp;的下标从 <strong>1</strong>&nbsp;开始的二进制表示。我们说一个整数&nbsp;<code>num</code>&nbsp;的 <strong>价值</strong>&nbsp;是满足&nbsp;<code>i % x == 0</code> 且&nbsp;<code><font face=\"monospace\">s[i]</font></code>&nbsp;是 <strong>设置位</strong>&nbsp;的 <code>i</code>&nbsp;的数目。</p>\n\n<p>请你返回<strong>&nbsp;最大</strong>&nbsp;整数<em>&nbsp;</em><code>num</code>&nbsp;，满足从 <code>1</code>&nbsp;到 <code>num</code>&nbsp;的所有整数的 <strong>价值</strong>&nbsp;和小于等于 <code>k</code>&nbsp;。</p>\n\n<p><b>注意：</b></p>\n\n<ul>\n\t<li>一个整数二进制表示下 <strong>设置位</strong>&nbsp;是值为 <code>1</code>&nbsp;的数位。</li>\n\t<li>一个整数的二进制表示下标从右到左编号，比方说如果&nbsp;<code>s == 11100</code>&nbsp;，那么&nbsp;<code>s[4] == 1</code> 且&nbsp;<code>s[2] == 0</code>&nbsp;。</li>\n</ul>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>k = 9, x = 1\n<b>输出：</b>6\n<b>解释：</b>数字 1 ，2 ，3 ，4 ，5 和 6 二进制表示分别为 \"1\" ，\"10\" ，\"11\" ，\"100\" ，\"101\" 和 \"110\" 。\n由于 x 等于 1 ，每个数字的价值分别为所有设置位的数目。\n这些数字的所有设置位数目总数是 9 ，所以前 6 个数字的价值和为 9 。\n所以答案为 6 。</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>k = 7, x = 2\n<b>输出：</b>9\n<b>解释：</b>由于 x 等于 2 ，我们检查每个数字的偶数位。\n2 和 3 在二进制表示下的第二个数位为设置位，所以它们的价值和为 2 。\n6 和 7 在二进制表示下的第二个数位为设置位，所以它们的价值和为 2 。\n8 和 9 在二进制表示下的第四个数位为设置位但第二个数位不是设置位，所以它们的价值和为 2 。\n数字 1 ，4 和 5 在二进制下偶数位都不是设置位，所以它们的价值和为 0 。\n10 在二进制表示下的第二个数位和第四个数位都是设置位，所以它的价值为 2 。\n前 9 个数字的价值和为 6 。\n前 10 个数字的价值和为 8，超过了 k = 7 ，所以答案为 9 。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k &lt;= 10<sup>15</sup></code></li>\n\t<li><code>1 &lt;= x &lt;= 8</code></li>\n</ul>\n",
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