leetcode-problemset/leetcode-cn/originData/count-paths-with-the-given-xor-value.json

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        "question": {
            "questionId": "3659",
            "questionFrontendId": "3393",
            "categoryTitle": "Algorithms",
            "boundTopicId": 3025425,
            "title": "Count Paths With the Given XOR Value",
            "titleSlug": "count-paths-with-the-given-xor-value",
            "content": "<p>You are given a 2D integer array <code>grid</code> with size <code>m x n</code>. You are also given an integer <code>k</code>.</p>\n\n<p>Your task is to calculate the number of paths you can take from the top-left cell <code>(0, 0)</code> to the bottom-right cell <code>(m - 1, n - 1)</code> satisfying the following <strong>constraints</strong>:</p>\n\n<ul>\n\t<li>You can either move to the right or down. Formally, from the cell <code>(i, j)</code> you may move to the cell <code>(i, j + 1)</code> or to the cell <code>(i + 1, j)</code> if the target cell <em>exists</em>.</li>\n\t<li>The <code>XOR</code> of all the numbers on the path must be <strong>equal</strong> to <code>k</code>.</li>\n</ul>\n\n<p>Return the total number of such paths.</p>\n\n<p>Since the answer can be very large, return the result <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\">grid = [[2, 1, 5], [7, 10, 0], [12, 6, 4]], k = 11</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">3</span></p>\n\n<p><strong>Explanation:</strong>&nbsp;</p>\n\n<p>The 3 paths are:</p>\n\n<ul>\n\t<li><code>(0, 0) &rarr; (1, 0) &rarr; (2, 0) &rarr; (2, 1) &rarr; (2, 2)</code></li>\n\t<li><code>(0, 0) &rarr; (1, 0) &rarr; (1, 1) &rarr; (1, 2) &rarr; (2, 2)</code></li>\n\t<li><code>(0, 0) &rarr; (0, 1) &rarr; (1, 1) &rarr; (2, 1) &rarr; (2, 2)</code></li>\n</ul>\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\">grid = [[1, 3, 3, 3], [0, 3, 3, 2], [3, 0, 1, 1]], k = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The 5 paths are:</p>\n\n<ul>\n\t<li><code>(0, 0) &rarr; (1, 0) &rarr; (2, 0) &rarr; (2, 1) &rarr; (2, 2) &rarr; (2, 3)</code></li>\n\t<li><code>(0, 0) &rarr; (1, 0) &rarr; (1, 1) &rarr; (2, 1) &rarr; (2, 2) &rarr; (2, 3)</code></li>\n\t<li><code>(0, 0) &rarr; (1, 0) &rarr; (1, 1) &rarr; (1, 2) &rarr; (1, 3) &rarr; (2, 3)</code></li>\n\t<li><code>(0, 0) &rarr; (0, 1) &rarr; (1, 1) &rarr; (1, 2) &rarr; (2, 2) &rarr; (2, 3)</code></li>\n\t<li><code>(0, 0) &rarr; (0, 1) &rarr; (0, 2) &rarr; (1, 2) &rarr; (2, 2) &rarr; (2, 3)</code></li>\n</ul>\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\">grid = [[1, 1, 1, 2], [3, 0, 3, 2], [3, 0, 2, 2]], k = 10</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">0</span></p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= m == grid.length &lt;= 300</code></li>\n\t<li><code>1 &lt;= n == grid[r].length &lt;= 300</code></li>\n\t<li><code>0 &lt;= grid[r][c] &lt; 16</code></li>\n\t<li><code>0 &lt;= k &lt; 16</code></li>\n</ul>\n",
            "translatedTitle": "统计异或值为给定值的路径数目",
            "translatedContent": "<p>给你一个大小为 <code>m x n</code>&nbsp;的二维整数数组&nbsp;<code>grid</code>&nbsp;和一个整数&nbsp;<code>k</code>&nbsp;。</p>\n\n<p>你的任务是统计满足以下 <strong>条件</strong> 且从左上格子&nbsp;<code>(0, 0)</code>&nbsp;出发到达右下格子&nbsp;<code>(m - 1, n - 1)</code>&nbsp;的路径数目：</p>\n\n<ul>\n\t<li>每一步你可以向右或者向下走，也就是如果格子存在的话，可以从格子&nbsp;<code>(i, j)</code>&nbsp;走到格子&nbsp;<code>(i, j + 1)</code>&nbsp;或者格子&nbsp;<code>(i + 1, j)</code>&nbsp;。</li>\n\t<li>路径上经过的所有数字&nbsp;<code>XOR</code>&nbsp;异或值必须 <strong>等于</strong>&nbsp;<code>k</code>&nbsp;。</li>\n</ul>\n\n<p>请你返回满足上述条件的路径总数。</p>\n\n<p>由于答案可能很大，请你将答案对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;<strong>取余</strong> 后返回。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>grid = [[2, 1, 5], [7, 10, 0], [12, 6, 4]], k = 11</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>3</span></p>\n\n<p><b>解释：</b></p>\n\n<p>3 条路径分别为：</p>\n\n<ul>\n\t<li><code>(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2)</code></li>\n\t<li><code>(0, 0) → (1, 0) → (1, 1) → (1, 2) → (2, 2)</code></li>\n\t<li><code>(0, 0) → (0, 1) → (1, 1) → (2, 1) → (2, 2)</code></li>\n</ul>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>grid = [[1, 3, 3, 3], [0, 3, 3, 2], [3, 0, 1, 1]], k = 2</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>5</span></p>\n\n<p><b>解释：</b></p>\n\n<p>5 条路径分别为：</p>\n\n<ul>\n\t<li><code>(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2) → (2, 3)</code></li>\n\t<li><code>(0, 0) → (1, 0) → (1, 1) → (2, 1) → (2, 2) → (2, 3)</code></li>\n\t<li><code>(0, 0) → (1, 0) → (1, 1) → (1, 2) → (1, 3) → (2, 3)</code></li>\n\t<li><code>(0, 0) → (0, 1) → (1, 1) → (1, 2) → (2, 2) → (2, 3)</code></li>\n\t<li><code>(0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2) → (2, 3)</code></li>\n</ul>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>grid = [[1, 1, 1, 2], [3, 0, 3, 2], [3, 0, 2, 2]], k = 10</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>0</span></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;= m == grid.length &lt;= 300</code></li>\n\t<li><code>1 &lt;= n == grid[r].length &lt;= 300</code></li>\n\t<li><code>0 &lt;= grid[r][c] &lt; 16</code></li>\n\t<li><code>0 &lt;= k &lt; 16</code></li>\n</ul>\n",
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