leetcode-problemset/leetcode-cn/originData/apply-operations-on-array-to-maximize-sum-of-squares.json

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            "title": "Apply Operations on Array to Maximize Sum of Squares",
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            "content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> and a <strong>positive</strong> integer <code>k</code>.</p>\n\n<p>You can do the following operation on the array <strong>any</strong> number of times:</p>\n\n<ul>\n\t<li>Choose any two distinct indices <code>i</code> and <code>j</code> and <strong>simultaneously</strong> update the values of <code>nums[i]</code> to <code>(nums[i] AND nums[j])</code> and <code>nums[j]</code> to <code>(nums[i] OR nums[j])</code>. Here, <code>OR</code> denotes the bitwise <code>OR</code> operation, and <code>AND</code> denotes the bitwise <code>AND</code> operation.</li>\n</ul>\n\n<p>You have to choose <code>k</code> elements from the final array and calculate the sum of their <strong>squares</strong>.</p>\n\n<p>Return <em>the <strong>maximum</strong> sum of squares you can achieve</em>.</p>\n\n<p>Since the answer can 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<pre>\n<strong>Input:</strong> nums = [2,6,5,8], k = 2\n<strong>Output:</strong> 261\n<strong>Explanation:</strong> We can do the following operations on the array:\n- Choose i = 0 and j = 3, then change nums[0] to (2 AND 8) = 0 and nums[3] to (2 OR 8) = 10. The resulting array is nums = [0,6,5,10].\n- Choose i = 2 and j = 3, then change nums[2] to (5 AND 10) = 0 and nums[3] to (5 OR 10) = 15. The resulting array is nums = [0,6,0,15].\nWe can choose the elements 15 and 6 from the final array. The sum of squares is 15<sup>2</sup> + 6<sup>2</sup> = 261.\nIt can be shown that this is the maximum value we can get.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [4,5,4,7], k = 3\n<strong>Output:</strong> 90\n<strong>Explanation:</strong> We do not need to apply any operations.\nWe can choose the elements 7, 5, and 4 with a sum of squares: 7<sup>2</sup> + 5<sup>2</sup> + 4<sup>2</sup> = 90.\nIt can be shown that this is the maximum value we can get.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "对数组执行操作使平方和最大",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>nums</code>&nbsp;和一个 <strong>正</strong>&nbsp;整数&nbsp;<code>k</code>&nbsp;。</p>\n\n<p>你可以对数组执行以下操作 <strong>任意次</strong>&nbsp;：</p>\n\n<ul>\n\t<li>选择两个互不相同的下标&nbsp;<code>i</code> 和&nbsp;<code>j</code>&nbsp;，<strong>同时</strong>&nbsp;将&nbsp;<code>nums[i]</code>&nbsp;更新为&nbsp;<code>(nums[i] AND nums[j])</code> 且将&nbsp;<code>nums[j]</code>&nbsp;更新为&nbsp;<code>(nums[i] OR nums[j])</code>&nbsp;，<code>OR</code>&nbsp;表示按位 <strong>或</strong>&nbsp;运算，<code>AND</code>&nbsp;表示按位 <strong>与</strong>&nbsp;运算。</li>\n</ul>\n\n<p>你需要从最终的数组里选择&nbsp;<code>k</code>&nbsp;个元素，并计算它们的 <strong>平方</strong>&nbsp;之和。</p>\n\n<p>请你返回你可以得到的 <strong>最大</strong>&nbsp;平方和。</p>\n\n<p>由于答案可能会很大，将答案对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;<strong>取余</strong>&nbsp;后返回。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [2,6,5,8], k = 2\n<b>输出：</b>261\n<b>解释：</b>我们可以对数组执行以下操作：\n- 选择 i = 0 和 j = 3 ，同时将 nums[0] 变为 (2 AND 8) = 0 且 nums[3] 变为 (2 OR 8) = 10 ，结果数组为 nums = [0,6,5,10] 。\n- 选择 i = 2 和 j = 3 ，同时将 nums[2] 变为 (5 AND 10) = 0 且 nums[3] 变为 (5 OR 10) = 15 ，结果数组为 nums = [0,6,0,15] 。\n从最终数组里选择元素 15 和 6 ，平方和为 15<sup>2</sup> + 6<sup>2</sup> = 261 。\n261 是可以得到的最大结果。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [4,5,4,7], k = 3\n<b>输出：</b>90\n<b>解释：</b>不需要执行任何操作。\n选择元素 7 ，5 和 4 ，平方和为 7<sup>2</sup> + 5<sup>2</sup> + 4<sup>2</sup> = 90 。\n90 是可以得到的最大结果。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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