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            "title": "Number of Ways to Rearrange Sticks With K Sticks Visible",
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            "content": "<p>There are <code>n</code> uniquely-sized sticks whose lengths are integers from <code>1</code> to <code>n</code>. You want to arrange the sticks such that <strong>exactly</strong> <code>k</code>&nbsp;sticks are <strong>visible</strong> from the left. A stick&nbsp;is <strong>visible</strong> from the left if there are no <strong>longer</strong>&nbsp;sticks to the <strong>left</strong> of it.</p>\n\n<ul>\n\t<li>For example, if the sticks are arranged <code>[<u>1</u>,<u>3</u>,2,<u>5</u>,4]</code>, then the sticks with lengths <code>1</code>, <code>3</code>, and <code>5</code> are visible from the left.</li>\n</ul>\n\n<p>Given <code>n</code> and <code>k</code>, return <em>the <strong>number</strong> of such arrangements</em>. Since the answer may be large, return it <strong>modulo</strong> <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 = 3, k = 2\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> [<u>1</u>,<u>3</u>,2], [<u>2</u>,<u>3</u>,1], and [<u>2</u>,1,<u>3</u>] are the only arrangements such that exactly 2 sticks are visible.\nThe visible sticks are underlined.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5, k = 5\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> [<u>1</u>,<u>2</u>,<u>3</u>,<u>4</u>,<u>5</u>] is the only arrangement such that all 5 sticks are visible.\nThe visible sticks are underlined.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 20, k = 11\n<strong>Output:</strong> 647427950\n<strong>Explanation:</strong> There are 647427950 (mod 10<sup>9 </sup>+ 7) ways to rearrange the sticks such that exactly 11 sticks are visible.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 1000</code></li>\n\t<li><code>1 &lt;= k &lt;= n</code></li>\n</ul>\n",
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