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"categoryTitle": "Algorithms",
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"title": "Concatenation of Consecutive Binary Numbers",
"titleSlug": "concatenation-of-consecutive-binary-numbers",
"content": "<p>Given an integer <code>n</code>, return <em>the <strong>decimal value</strong> of the binary string formed by concatenating the binary representations of </em><code>1</code><em> to </em><code>n</code><em> in order, <strong>modulo </strong></em><code>10<sup>9 </sup>+ 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1\n<strong>Output:</strong> 1\n<strong>Explanation: </strong>&quot;1&quot; in binary corresponds to the decimal value 1. \n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3\n<strong>Output:</strong> 27\n<strong>Explanation: </strong>In binary, 1, 2, and 3 corresponds to &quot;1&quot;, &quot;10&quot;, and &quot;11&quot;.\nAfter concatenating them, we have &quot;11011&quot;, which corresponds to the decimal value 27.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 12\n<strong>Output:</strong> 505379714\n<strong>Explanation</strong>: The concatenation results in &quot;1101110010111011110001001101010111100&quot;.\nThe decimal value of that is 118505380540.\nAfter modulo 10<sup>9</sup> + 7, the result is 505379714.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
"translatedTitle": "连接连续二进制数字",
"translatedContent": "<p>给你一个整数 <code>n</code> ,请你将 <code>1</code> 到 <code>n</code> 的二进制表示连接起来,并返回连接结果对应的 <strong>十进制</strong> 数字对 <code>10<sup>9</sup> + 7</code> 取余的结果。</p>\n\n<p> </p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><b>输入:</b>n = 1\n<b>输出:</b>1\n<strong>解释:</strong>二进制的 \"1\" 对应着十进制的 1 。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><b>输入:</b>n = 3\n<b>输出:</b>27\n<strong>解释:</strong>二进制下12 和 3 分别对应 \"1\" \"10\" 和 \"11\" 。\n将它们依次连接我们得到 \"11011\" ,对应着十进制的 27 。\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre><b>输入:</b>n = 12\n<b>输出:</b>505379714\n<b>解释:</b>连接结果为 \"1101110010111011110001001101010111100\" 。\n对应的十进制数字为 118505380540 。\n对 10<sup>9</sup> + 7 取余后,结果为 505379714 。\n</pre>\n\n<p> </p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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