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

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    "data": {
        "question": {
            "questionId": "3240",
            "questionFrontendId": "3007",
            "categoryTitle": "Algorithms",
            "boundTopicId": 2600612,
            "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>. The price of a number&nbsp;<code>num</code> is calculated by the count of <span data-keyword=\"set-bit\">set bits</span> at positions <code>x</code>, <code>2x</code>, <code>3x</code>, etc., in its binary representation, starting from the least significant bit. The following table contains examples of how price is calculated.</p>\n\n<table border=\"1\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th>x</th>\n\t\t\t<th>num</th>\n\t\t\t<th>Binary Representation</th>\n\t\t\t<th>Price</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>13</td>\n\t\t\t<td><u>0</u><u>0</u><u>0</u><u>0</u><u>0</u><strong><u>1</u></strong><strong><u>1</u></strong><u>0</u><strong><u>1</u></strong></td>\n\t\t\t<td>3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>13</td>\n\t\t\t<td>0<u>0</u>0<u>0</u>0<strong><u>1</u></strong>1<u>0</u>1</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>233</td>\n\t\t\t<td>0<strong><u>1</u></strong>1<strong><u>1</u></strong>0<strong><u>1</u></strong>0<u>0</u>1</td>\n\t\t\t<td>3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>13</td>\n\t\t\t<td><u>0</u>00<u>0</u>01<strong><u>1</u></strong>01</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>362</td>\n\t\t\t<td><strong><u>1</u></strong>01<strong><u>1</u></strong>01<u>0</u>10</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t</tbody>\n</table>\n\n<p>The&nbsp;<strong>accumulated price</strong>&nbsp;of&nbsp;<code>num</code>&nbsp;is the <b>total</b>&nbsp;price of&nbsp;numbers from <code>1</code> to <code>num</code>. <code>num</code>&nbsp;is considered&nbsp;<strong>cheap</strong>&nbsp;if its accumulated price&nbsp;is less than or equal to <code>k</code>.</p>\n\n<p>Return the <b>greatest</b>&nbsp;cheap number.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">k = 9, x = 1</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">6</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>As shown in the table below, <code>6</code> is the greatest cheap number.</p>\n\n<table border=\"1\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th>x</th>\n\t\t\t<th>num</th>\n\t\t\t<th>Binary Representation</th>\n\t\t\t<th>Price</th>\n\t\t\t<th>Accumulated Price</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>1</td>\n\t\t\t<td><u>0</u><u>0</u><strong><u>1</u></strong></td>\n\t\t\t<td>1</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>2</td>\n\t\t\t<td><u>0</u><strong><u>1</u></strong><u>0</u></td>\n\t\t\t<td>1</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>3</td>\n\t\t\t<td><u>0</u><strong><u>1</u></strong><strong><u>1</u></strong></td>\n\t\t\t<td>2</td>\n\t\t\t<td>4</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>4</td>\n\t\t\t<td><strong><u>1</u></strong><u>0</u><u>0</u></td>\n\t\t\t<td>1</td>\n\t\t\t<td>5</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>5</td>\n\t\t\t<td><strong><u>1</u></strong><u>0</u><strong><u>1</u></strong></td>\n\t\t\t<td>2</td>\n\t\t\t<td>7</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>6</td>\n\t\t\t<td><strong><u>1</u></strong><strong><u>1</u></strong><u>0</u></td>\n\t\t\t<td>2</td>\n\t\t\t<td>9</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>7</td>\n\t\t\t<td><strong><u>1</u></strong><strong><u>1</u></strong><strong><u>1</u></strong></td>\n\t\t\t<td>3</td>\n\t\t\t<td>12</td>\n\t\t</tr>\n\t</tbody>\n</table>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">k = 7, x = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">9</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>As shown in the table below, <code>9</code> is the greatest cheap number.</p>\n\n<table border=\"1\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th>x</th>\n\t\t\t<th>num</th>\n\t\t\t<th>Binary Representation</th>\n\t\t\t<th>Price</th>\n\t\t\t<th>Accumulated Price</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>1</td>\n\t\t\t<td><u>0</u>0<u>0</u>1</td>\n\t\t\t<td>0</td>\n\t\t\t<td>0</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>2</td>\n\t\t\t<td><u>0</u>0<strong><u>1</u></strong>0</td>\n\t\t\t<td>1</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>3</td>\n\t\t\t<td><u>0</u>0<strong><u>1</u></strong>1</td>\n\t\t\t<td>1</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>4</td>\n\t\t\t<td><u>0</u>1<u>0</u>0</td>\n\t\t\t<td>0</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>5</td>\n\t\t\t<td><u>0</u>1<u>0</u>1</td>\n\t\t\t<td>0</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>6</td>\n\t\t\t<td><u>0</u>1<strong><u>1</u></strong>0</td>\n\t\t\t<td>1</td>\n\t\t\t<td>3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>7</td>\n\t\t\t<td><u>0</u>1<strong><u>1</u></strong>1</td>\n\t\t\t<td>1</td>\n\t\t\t<td>4</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>8</td>\n\t\t\t<td><strong><u>1</u></strong>0<u>0</u>0</td>\n\t\t\t<td>1</td>\n\t\t\t<td>5</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>9</td>\n\t\t\t<td><strong><u>1</u></strong>0<u>0</u>1</td>\n\t\t\t<td>1</td>\n\t\t\t<td>6</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>10</td>\n\t\t\t<td><strong><u>1</u></strong>0<strong><u>1</u></strong>0</td>\n\t\t\t<td>2</td>\n\t\t\t<td>8</td>\n\t\t</tr>\n\t</tbody>\n</table>\n</div>\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;。整数&nbsp;<code>num</code>&nbsp;的价值是它的二进制表示中在&nbsp;<code>x</code>，<code>2x</code>，<code>3x</code>&nbsp;等位置处&nbsp;<strong><span data-keyword=\"set-bit\">设置位</span></strong>&nbsp;的数目（从最低有效位开始）。下面的表格包含了如何计算价值的例子。</p>\n\n<table border=\"1\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th>x</th>\n\t\t\t<th>num</th>\n\t\t\t<th>Binary Representation</th>\n\t\t\t<th>Price</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>13</td>\n\t\t\t<td><u>0</u><u>0</u><u>0</u><u>0</u><u>0</u><strong><u>1</u></strong><strong><u>1</u></strong><u>0</u><strong><u>1</u></strong></td>\n\t\t\t<td>3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>13</td>\n\t\t\t<td>0<u>0</u>0<u>0</u>0<strong><u>1</u></strong>1<u>0</u>1</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>233</td>\n\t\t\t<td>0<strong><u>1</u></strong>1<strong><u>1</u></strong>0<strong><u>1</u></strong>0<u>0</u>1</td>\n\t\t\t<td>3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>13</td>\n\t\t\t<td><u>0</u>00<u>0</u>01<strong><u>1</u></strong>01</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>362</td>\n\t\t\t<td><strong><u>1</u></strong>01<strong><u>1</u></strong>01<u>0</u>10</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p><code>num</code>&nbsp;的 <strong>累加价值</strong> 是从&nbsp;<code>1</code>&nbsp;到&nbsp;<code>num</code>&nbsp;的数字的 <strong>总</strong> 价值。如果&nbsp;<code>num</code>&nbsp;的累加价值小于或等于&nbsp;<code>k</code>&nbsp;则被认为是 <strong>廉价</strong> 的。</p>\n\n<p>请你返回<strong>&nbsp;最大</strong>&nbsp;的廉价数字。</p>\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>由下表所示，6 是最大的廉价数字。\n</pre>\n\n<table border=\"1\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th>x</th>\n\t\t\t<th>num</th>\n\t\t\t<th>Binary Representation</th>\n\t\t\t<th>Price</th>\n\t\t\t<th>Accumulated Price</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>1</td>\n\t\t\t<td><u>0</u><u>0</u><strong><u>1</u></strong></td>\n\t\t\t<td>1</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>2</td>\n\t\t\t<td><u>0</u><strong><u>1</u></strong><u>0</u></td>\n\t\t\t<td>1</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>3</td>\n\t\t\t<td><u>0</u><strong><u>1</u></strong><strong><u>1</u></strong></td>\n\t\t\t<td>2</td>\n\t\t\t<td>4</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>4</td>\n\t\t\t<td><strong><u>1</u></strong><u>0</u><u>0</u></td>\n\t\t\t<td>1</td>\n\t\t\t<td>5</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>5</td>\n\t\t\t<td><strong><u>1</u></strong><u>0</u><strong><u>1</u></strong></td>\n\t\t\t<td>2</td>\n\t\t\t<td>7</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>6</td>\n\t\t\t<td><strong><u>1</u></strong><strong><u>1</u></strong><u>0</u></td>\n\t\t\t<td>2</td>\n\t\t\t<td>9</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>7</td>\n\t\t\t<td><strong><u>1</u></strong><strong><u>1</u></strong><strong><u>1</u></strong></td>\n\t\t\t<td>3</td>\n\t\t\t<td>12</td>\n\t\t</tr>\n\t</tbody>\n</table>\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>由下表所示，9 是最大的廉价数字。\n</pre>\n\n<table border=\"1\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th>x</th>\n\t\t\t<th>num</th>\n\t\t\t<th>Binary Representation</th>\n\t\t\t<th>Price</th>\n\t\t\t<th>Accumulated Price</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>1</td>\n\t\t\t<td><u>0</u>0<u>0</u>1</td>\n\t\t\t<td>0</td>\n\t\t\t<td>0</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>2</td>\n\t\t\t<td><u>0</u>0<strong><u>1</u></strong>0</td>\n\t\t\t<td>1</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>3</td>\n\t\t\t<td><u>0</u>0<strong><u>1</u></strong>1</td>\n\t\t\t<td>1</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>4</td>\n\t\t\t<td><u>0</u>1<u>0</u>0</td>\n\t\t\t<td>0</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>5</td>\n\t\t\t<td><u>0</u>1<u>0</u>1</td>\n\t\t\t<td>0</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>6</td>\n\t\t\t<td><u>0</u>1<strong><u>1</u></strong>0</td>\n\t\t\t<td>1</td>\n\t\t\t<td>3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>7</td>\n\t\t\t<td><u>0</u>1<strong><u>1</u></strong>1</td>\n\t\t\t<td>1</td>\n\t\t\t<td>4</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>8</td>\n\t\t\t<td><strong><u>1</u></strong>0<u>0</u>0</td>\n\t\t\t<td>1</td>\n\t\t\t<td>5</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>9</td>\n\t\t\t<td><strong><u>1</u></strong>0<u>0</u>1</td>\n\t\t\t<td>1</td>\n\t\t\t<td>6</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>10</td>\n\t\t\t<td><strong><u>1</u></strong>0<strong><u>1</u></strong>0</td>\n\t\t\t<td>2</td>\n\t\t\t<td>8</td>\n\t\t</tr>\n\t</tbody>\n</table>\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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