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"categoryTitle": "Algorithms",
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"title": "Maximum and Minimum Sums of at Most Size K Subsequences",
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"content": "<p>You are given an integer array <code>nums</code> and a positive integer <code>k</code>. Return the sum of the <strong>maximum</strong> and <strong>minimum</strong> elements of all <strong><span data-keyword=\"subsequence-sequence-nonempty\">subsequences</span></strong> of <code>nums</code> with <strong>at most</strong> <code>k</code> elements.</p>\n\n<p>Since the answer may be very 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<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,2,3], k = 2</span></p>\n\n<p><strong>Output:</strong> 24</p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The subsequences of <code>nums</code> with at most 2 elements are:</p>\n\n<table style=\"border: 1px solid black;\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th style=\"border: 1px solid black;\"><b>Subsequence </b></th>\n\t\t\t<th style=\"border: 1px solid black;\">Minimum</th>\n\t\t\t<th style=\"border: 1px solid black;\">Maximum</th>\n\t\t\t<th style=\"border: 1px solid black;\">Sum</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[1]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">1</td>\n\t\t\t<td style=\"border: 1px solid black;\">1</td>\n\t\t\t<td style=\"border: 1px solid black;\">2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[2]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">2</td>\n\t\t\t<td style=\"border: 1px solid black;\">2</td>\n\t\t\t<td style=\"border: 1px solid black;\">4</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[3]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">3</td>\n\t\t\t<td style=\"border: 1px solid black;\">3</td>\n\t\t\t<td style=\"border: 1px solid black;\">6</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[1, 2]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">1</td>\n\t\t\t<td style=\"border: 1px solid black;\">2</td>\n\t\t\t<td style=\"border: 1px solid black;\">3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[1, 3]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">1</td>\n\t\t\t<td style=\"border: 1px solid black;\">3</td>\n\t\t\t<td style=\"border: 1px solid black;\">4</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[2, 3]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">2</td>\n\t\t\t<td style=\"border: 1px solid black;\">3</td>\n\t\t\t<td style=\"border: 1px solid black;\">5</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><strong>Final Total</strong></td>\n\t\t\t<td style=\"border: 1px solid black;\">&nbsp;</td>\n\t\t\t<td style=\"border: 1px solid black;\">&nbsp;</td>\n\t\t\t<td style=\"border: 1px solid black;\">24</td>\n\t\t</tr>\n\t</tbody>\n</table>\n\n<p>The output would be 24.</p>\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\">nums = [5,0,6], k = 1</span></p>\n\n<p><strong>Output:</strong> 2<span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation: </strong></p>\n\n<p>For subsequences with exactly 1 element, the minimum and maximum values are the element itself. Therefore, the total is <code>5 + 5 + 0 + 0 + 6 + 6 = 22</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,1,1], k = 2</span></p>\n\n<p><strong>Output:</strong> 12</p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The subsequences <code>[1, 1]</code> and <code>[1]</code> each appear 3 times. For all of them, the minimum and maximum are both 1. Thus, the total is 12.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code><font face=\"monospace\">1 &lt;= k &lt;= min(70, nums.length)</font></code></li>\n</ul>\n",
"translatedTitle": "最多 K 个元素的子序列的最值之和",
"translatedContent": "<p>给你一个整数数组 <code>nums</code> 和一个正整数 <code>k</code>,返回所有长度最多为 <code>k</code> 的 <strong>子序列</strong> 中&nbsp;<strong>最大值&nbsp;</strong>与&nbsp;<strong>最小值&nbsp;</strong>之和的总和。</p>\n\n<p><strong>非空子序列</strong>&nbsp;是指从另一个数组中删除一些或不删除任何元素(且不改变剩余元素的顺序)得到的数组。</p>\n\n<p>由于答案可能非常大,请返回对 <code>10<sup>9</sup> + 7</code> 取余数的结果。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入:</strong> <span class=\"example-io\">nums = [1,2,3], k = 2</span></p>\n\n<p><strong>输出:</strong> 24</p>\n\n<p><strong>解释:</strong></p>\n\n<p>数组 <code>nums</code> 中所有长度最多为 2 的子序列如下:</p>\n\n<table style=\"border: 1px solid black; border-collapse: collapse;\">\n\t<thead>\n\t\t<tr>\n\t\t\t<th style=\"border: 1px solid black;\">子序列</th>\n\t\t\t<th style=\"border: 1px solid black;\">最小值</th>\n\t\t\t<th style=\"border: 1px solid black;\">最大值</th>\n\t\t\t<th style=\"border: 1px solid black;\">和</th>\n\t\t</tr>\n\t</thead>\n\t<tbody>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[1]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">1</td>\n\t\t\t<td style=\"border: 1px solid black;\">1</td>\n\t\t\t<td style=\"border: 1px solid black;\">2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[2]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">2</td>\n\t\t\t<td style=\"border: 1px solid black;\">2</td>\n\t\t\t<td style=\"border: 1px solid black;\">4</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[3]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">3</td>\n\t\t\t<td style=\"border: 1px solid black;\">3</td>\n\t\t\t<td style=\"border: 1px solid black;\">6</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[1, 2]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">1</td>\n\t\t\t<td style=\"border: 1px solid black;\">2</td>\n\t\t\t<td style=\"border: 1px solid black;\">3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[1, 3]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">1</td>\n\t\t\t<td style=\"border: 1px solid black;\">3</td>\n\t\t\t<td style=\"border: 1px solid black;\">4</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><code>[2, 3]</code></td>\n\t\t\t<td style=\"border: 1px solid black;\">2</td>\n\t\t\t<td style=\"border: 1px solid black;\">3</td>\n\t\t\t<td style=\"border: 1px solid black;\">5</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"border: 1px solid black;\"><strong>总和</strong></td>\n\t\t\t<td style=\"border: 1px solid black;\">&nbsp;</td>\n\t\t\t<td style=\"border: 1px solid black;\">&nbsp;</td>\n\t\t\t<td style=\"border: 1px solid black;\">24</td>\n\t\t</tr>\n\t</tbody>\n</table>\n\n<p>因此,输出为 24。</p>\n</div>\n\n<p><strong>示例 2</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入:</strong> <span class=\"example-io\">nums = [5,0,6], k = 1</span></p>\n\n<p><strong>输出:</strong> 22</p>\n\n<p><strong>解释:</strong></p>\n\n<p>对于长度恰好为 1 的子序列,最小值和最大值均为元素本身。因此,总和为 <code>5 + 5 + 0 + 0 + 6 + 6 = 22</code>。</p>\n</div>\n\n<p><strong>示例 3</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入:</strong> <span class=\"example-io\">nums = [1,1,1], k = 2</span></p>\n\n<p><strong>输出:</strong> 12</p>\n\n<p><strong>解释:</strong></p>\n\n<p>子序列 <code>[1, 1]</code> 和 <code>[1]</code> 各出现 3 次。对于所有这些子序列,最小值和最大值均为 1。因此总和为 12。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= min(100, nums.length)</code></li>\n</ul>\n",
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