leetcode-problemset/leetcode-cn/originData/number-of-ways-to-rearrange-sticks-with-k-sticks-visible.json

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            "title": "Number of Ways to Rearrange Sticks With K Sticks Visible",
            "titleSlug": "number-of-ways-to-rearrange-sticks-with-k-sticks-visible",
            "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 class=\"example\">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 class=\"example\">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 class=\"example\">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",
            "translatedTitle": "恰有 K 根木棍可以看到的排列数目",
            "translatedContent": "<p>有 <code>n</code> 根长度互不相同的木棍，长度为从 <code>1</code> 到 <code>n</code> 的整数。请你将这些木棍排成一排，并满足从左侧 <strong>可以看到</strong> <strong>恰好</strong> <code>k</code> 根木棍。从左侧 <strong>可以看到</strong> 木棍的前提是这个木棍的 <strong>左侧</strong> 不存在比它 <strong>更长的</strong> 木棍。</p>\n\n<ul>\n\t<li>例如，如果木棍排列为 <code>[<em><strong>1</strong></em>,<em><strong>3</strong></em>,2,<em><strong>5</strong></em>,4]</code> ，那么从左侧可以看到的就是长度分别为 <code>1</code>、<code>3</code> 、<code>5</code> 的木棍。</li>\n</ul>\n\n<p>给你 <code>n</code> 和 <code>k</code> ，返回符合题目要求的排列 <strong>数目</strong> 。由于答案可能很大，请返回对 <code>10<sup>9</sup> + 7</code> <strong>取余 </strong>的结果。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>n = 3, k = 2\n<strong>输出：</strong>3\n<strong>解释：</strong>[<strong><em>1</em></strong>,<strong><em>3</em></strong>,2], [<em><strong>2</strong></em>,<em><strong>3</strong></em>,1] 和 [<em><strong>2</strong></em>,1,<em><strong>3</strong></em>] 是仅有的能满足恰好 2 根木棍可以看到的排列。\n可以看到的木棍已经用粗体+斜体标识。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>n = 5, k = 5\n<strong>输出：</strong>1\n<strong>解释：</strong>[<em><strong>1</strong></em>,<em><strong>2</strong></em>,<em><strong>3</strong></em>,<em><strong>4</strong></em>,<em><strong>5</strong></em>] 是唯一一种能满足全部 5 根木棍可以看到的排列。\n可以看到的木棍已经用粗体+斜体标识。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><strong>输入：</strong>n = 20, k = 11\n<strong>输出：</strong>647427950\n<strong>解释：</strong>总共有 647427950 (mod 10<sup>9 </sup>+ 7) 种能满足恰好有 11 根木棍可以看到的排列。\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;= 1000</code></li>\n\t<li><code>1 &lt;= k &lt;= n</code></li>\n</ul>\n",
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