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"content": "<p>Bob is standing at cell <code>(0, 0)</code>, and he wants to reach <code>destination</code>: <code>(row, column)</code>. He can only travel <strong>right</strong> and <strong>down</strong>. You are going to help Bob by providing <strong>instructions</strong> for him to reach <code>destination</code>.</p>\n\n<p>The <strong>instructions</strong> are represented as a string, where each character is either:</p>\n\n<ul>\n\t<li><code>'H'</code>, meaning move horizontally (go <strong>right</strong>), or</li>\n\t<li><code>'V'</code>, meaning move vertically (go <strong>down</strong>).</li>\n</ul>\n\n<p>Multiple <strong>instructions</strong> will lead Bob to <code>destination</code>. For example, if <code>destination</code> is <code>(2, 3)</code>, both <code>"HHHVV"</code> and <code>"HVHVH"</code> are valid <strong>instructions</strong>.</p>\n\n<p>However, Bob is very picky. Bob has a lucky number <code>k</code>, and he wants the <code>k<sup>th</sup></code> <strong>lexicographically smallest instructions</strong> that will lead him to <code>destination</code>. <code>k</code> is <strong>1-indexed</strong>.</p>\n\n<p>Given an integer array <code>destination</code> and an integer <code>k</code>, return <em>the </em><code>k<sup>th</sup></code><em> <strong>lexicographically smallest instructions</strong> that will take Bob to </em><code>destination</code>.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/10/12/ex1.png\" style=\"width: 300px; height: 229px;\" /></p>\n\n<pre>\n<strong>Input:</strong> destination = [2,3], k = 1\n<strong>Output:</strong> "HHHVV"\n<strong>Explanation:</strong> All the instructions that reach (2, 3) in lexicographic order are as follows:\n["HHHVV", "HHVHV", "HHVVH", "HVHHV", "HVHVH", "HVVHH", "VHHHV", "VHHVH", "VHVHH", "VVHHH"].\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/10/12/ex2.png\" style=\"width: 300px; height: 229px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> destination = [2,3], k = 2\n<strong>Output:</strong> "HHVHV"\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/10/12/ex3.png\" style=\"width: 300px; height: 229px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> destination = [2,3], k = 3\n<strong>Output:</strong> "HHVVH"\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>destination.length == 2</code></li>\n\t<li><code>1 <= row, column <= 15</code></li>\n\t<li><code>1 <= k <= nCr(row + column, row)</code>, where <code>nCr(a, b)</code> denotes <code>a</code> choose <code>b</code>.</li>\n</ul>\n",
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"hints": [
"There are nCr(row + column, row) possible instructions to reach (row, column).",
"Try building the instructions one step at a time. How many instructions start with \"H\", and how does this compare with k?"
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