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"title": "Count Ways to Make Array With Product",
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"content": "<p>You are given a 2D integer array, <code>queries</code>. For each <code>queries[i]</code>, where <code>queries[i] = [n<sub>i</sub>, k<sub>i</sub>]</code>, find the number of different ways you can place positive integers into an array of size <code>n<sub>i</sub></code> such that the product of the integers is <code>k<sub>i</sub></code>. As the number of ways may be too large, the answer to the <code>i<sup>th</sup></code> query is the number of ways <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>Return <em>an integer array </em><code>answer</code><em> where </em><code>answer.length == queries.length</code><em>, and </em><code>answer[i]</code><em> is the answer to the </em><code>i<sup>th</sup></code><em> query.</em></p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> queries = [[2,6],[5,1],[73,660]]\n<strong>Output:</strong> [4,1,50734910]\n<strong>Explanation:</strong> Each query is independent.\n[2,6]: There are 4 ways to fill an array of size 2 that multiply to 6: [1,6], [2,3], [3,2], [6,1].\n[5,1]: There is 1 way to fill an array of size 5 that multiply to 1: [1,1,1,1,1].\n[73,660]: There are 1050734917 ways to fill an array of size 73 that multiply to 660. 1050734917 modulo 10<sup>9</sup> + 7 = 50734910.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> queries = [[1,1],[2,2],[3,3],[4,4],[5,5]]\n<strong>Output:</strong> [1,2,3,10,5]\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= queries.length <= 10<sup>4</sup> </code></li>\n\t<li><code>1 <= n<sub>i</sub>, k<sub>i</sub> <= 10<sup>4</sup></code></li>\n</ul>\n",
"translatedTitle": "生成乘积数组的方案数",
"translatedContent": "<p>给你一个二维整数数组 <code>queries</code> ，其中 <code>queries[i] = [n<sub>i</sub>, k<sub>i</sub>]</code> 。第 <code>i</code> 个查询 <code>queries[i]</code> 要求构造长度为 <code>n<sub>i</sub></code> 、每个元素都是正整数的数组，且满足所有元素的乘积为 <code>k<sub>i</sub></code><sub> </sub>，请你找出有多少种可行的方案。由于答案可能会很大，方案数需要对 <code>10<sup>9</sup> + 7</code> <strong>取余</strong> 。</p>\n\n<p>请你返回一个整数数组<em> </em><code>answer</code>，满足<em> </em><code>answer.length == queries.length</code> ，其中<em> </em><code>answer[i]</code>是第<em> </em><code>i</code> 个查询的结果。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>queries = [[2,6],[5,1],[73,660]]\n<b>输出：</b>[4,1,50734910]\n<b>解释：</b>每个查询之间彼此独立。\n[2,6]：总共有 4 种方案得到长度为 2 且乘积为 6 的数组：[1,6]，[2,3]，[3,2]，[6,1]。\n[5,1]：总共有 1 种方案得到长度为 5 且乘积为 1 的数组：[1,1,1,1,1]。\n[73,660]：总共有 1050734917 种方案得到长度为 73 且乘积为 660 的数组。1050734917 对 10<sup>9</sup> + 7 取余得到 50734910 。\n</pre>\n\n<p><strong>示例 2 ：</strong></p>\n\n<pre>\n<b>输入：</b>queries = [[1,1],[2,2],[3,3],[4,4],[5,5]]\n<b>输出：</b>[1,2,3,10,5]\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= queries.length <= 10<sup>4</sup> </code></li>\n\t<li><code>1 <= n<sub>i</sub>, k<sub>i</sub> <= 10<sup>4</sup></code></li>\n</ul>\n",
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