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"question": {
"questionId": "3192",
"questionFrontendId": "2939",
"categoryTitle": "Algorithms",
"boundTopicId": 2529055,
"title": "Maximum Xor Product",
"titleSlug": "maximum-xor-product",
"content": "<p>Given three integers <code>a</code>, <code>b</code>, and <code>n</code>, return <em>the <strong>maximum value</strong> of</em> <code>(a XOR x) * (b XOR x)</code> <em>where</em> <code>0 &lt;= x &lt; 2<sup>n</sup></code>.</p>\n\n<p>Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9 </sup>+ 7</code>.</p>\n\n<p><strong>Note</strong> that <code>XOR</code> is the bitwise XOR operation.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> a = 12, b = 5, n = 4\n<strong>Output:</strong> 98\n<strong>Explanation:</strong> For x = 2, (a XOR x) = 14 and (b XOR x) = 7. Hence, (a XOR x) * (b XOR x) = 98. \nIt can be shown that 98 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup><span style=\"font-size: 10.8333px;\">.</span>\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> a = 6, b = 7 , n = 5\n<strong>Output:</strong> 930\n<strong>Explanation:</strong> For x = 25, (a XOR x) = 31 and (b XOR x) = 30. Hence, (a XOR x) * (b XOR x) = 930.\nIt can be shown that 930 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>.</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> a = 1, b = 6, n = 3\n<strong>Output:</strong> 12\n<strong>Explanation:</strong> For x = 5, (a XOR x) = 4 and (b XOR x) = 3. Hence, (a XOR x) * (b XOR x) = 12.\nIt can be shown that 12 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>0 &lt;= a, b &lt; 2<sup>50</sup></code></li>\n\t<li><code>0 &lt;= n &lt;= 50</code></li>\n</ul>\n",
"translatedTitle": "最大异或乘积",
"translatedContent": "<p>给你三个整数&nbsp;<code>a</code>&nbsp;<code>b</code>&nbsp;和&nbsp;<code>n</code>&nbsp;,请你返回&nbsp;<code>(a XOR x) * (b XOR x)</code>&nbsp;的&nbsp;<strong>最大值</strong>&nbsp;且 <code>x</code>&nbsp;需要满足 <code>0 &lt;= x &lt; 2<sup>n</sup></code>。</p>\n\n<p>由于答案可能会很大,返回它对&nbsp;<code>10<sup>9 </sup>+ 7</code>&nbsp;<strong>取余</strong>&nbsp;后的结果。</p>\n\n<p><strong>注意</strong><code>XOR</code>&nbsp;是按位异或操作。</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>a = 12, b = 5, n = 4\n<b>输出:</b>98\n<b>解释:</b>当 x = 2 时,(a XOR x) = 14 且 (b XOR x) = 7 。所以,(a XOR x) * (b XOR x) = 98 。\n98 是所有满足 0 &lt;= x &lt; 2<sup>n </sup>中 (a XOR x) * (b XOR x) 的最大值。\n</pre>\n\n<p><strong class=\"example\">示例 2</strong></p>\n\n<pre>\n<b>输入:</b>a = 6, b = 7 , n = 5\n<b>输出:</b>930\n<b>解释:</b>当 x = 25 时,(a XOR x) = 31 且 (b XOR x) = 30 。所以,(a XOR x) * (b XOR x) = 930 。\n930 是所有满足 0 &lt;= x &lt; 2<sup>n </sup>中 (a XOR x) * (b XOR x) 的最大值。</pre>\n\n<p><strong class=\"example\">示例 3</strong></p>\n\n<pre>\n<b>输入:</b>a = 1, b = 6, n = 3\n<b>输出:</b>12\n<b>解释: </b>当 x = 5 时,(a XOR x) = 4 且 (b XOR x) = 3 。所以,(a XOR x) * (b XOR x) = 12 。\n12 是所有满足 0 &lt;= x &lt; 2<sup>n </sup>中 (a XOR x) * (b XOR x) 的最大值。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>0 &lt;= a, b &lt; 2<sup>50</sup></code></li>\n\t<li><code>0 &lt;= n &lt;= 50</code></li>\n</ul>\n",
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"For the <code>i<sup>th</sup></code> bit, if both <code>a</code> and <code>b</code> have the same value, we can always make <code>x</code>s <code>i<sup>th</sup></code> bit different from <code>a</code> and <code>b</code>, so <code>a ^ x</code> and <code>b ^ x</code> both have the <code>i<sup>th</sup></cod> bit set.",
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