You are given a positive integer primeFactors. You are asked to construct a positive integer n that satisfies the following conditions:
n (not necessarily distinct) is at most primeFactors.n is maximized. Note that a divisor of n is nice if it is divisible by every prime factor of n. For example, if n = 12, then its prime factors are [2,2,3], then 6 and 12 are nice divisors, while 3 and 4 are not.Return the number of nice divisors of n. Since that number can be too large, return it modulo 109 + 7.
Note that a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. The prime factors of a number n is a list of prime numbers such that their product equals n.
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Example 1:
\r\n\r\n\r\nInput: primeFactors = 5\r\nOutput: 6\r\nExplanation: 200 is a valid value of n.\r\nIt has 5 prime factors: [2,2,2,5,5], and it has 6 nice divisors: [10,20,40,50,100,200].\r\nThere is not other value of n that has at most 5 prime factors and more nice divisors.\r\n\r\n\r\n
Example 2:
\r\n\r\n\r\nInput: primeFactors = 8\r\nOutput: 18\r\n\r\n\r\n
\r\n
Constraints:
\r\n\r\n1 <= primeFactors <= 109给你一个正整数 primeFactors 。你需要构造一个正整数 n ，它满足以下条件：
n 质因数（质因数需要考虑重复的情况）的数目 不超过 primeFactors 个。n 好因子的数目最大化。如果 n 的一个因子可以被 n 的每一个质因数整除，我们称这个因子是 好因子 。比方说，如果 n = 12 ，那么它的质因数为 [2,2,3] ，那么 6 和 12 是好因子，但 3 和 4 不是。请你返回 n 的好因子的数目。由于答案可能会很大，请返回答案对 109 + 7 取余 的结果。
请注意，一个质数的定义是大于 1 ，且不能被分解为两个小于该数的自然数相乘。一个数 n 的质因子是将 n 分解为若干个质因子，且它们的乘积为 n 。
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示例 1：
\n\n\n输入：primeFactors = 5\n输出：6\n解释：200 是一个可行的 n 。\n它有 5 个质因子：[2,2,2,5,5] ，且有 6 个好因子：[10,20,40,50,100,200] 。\n不存在别的 n 有至多 5 个质因子，且同时有更多的好因子。\n\n\n
示例 2：
\n\n\n输入：primeFactors = 8\n输出：18\n\n\n
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提示：
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collections<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u6ce8\\u610f Python 2.7 \\u5c06\\u57282020\\u5e74\\u540e\\u4e0d\\u518d\\u7ef4\\u62a4<\\/a>\\u3002 \\u5982\\u60f3\\u4f7f\\u7528\\u6700\\u65b0\\u7248\\u7684Python\\uff0c\\u8bf7\\u9009\\u62e9Python 3\\u3002<\\/p>\"],\"c\":[\"C\",\" \\u7248\\u672c\\uff1a \\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528 \\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u5982\\u60f3\\u4f7f\\u7528\\u54c8\\u5e0c\\u8868\\u8fd0\\u7b97, \\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 uthash<\\/a>\\u3002 \\\"uthash.h\\\"\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5bfc\\u5165\\u3002\\u8bf7\\u770b\\u5982\\u4e0b\\u793a\\u4f8b:<\\/p>\\r\\n\\r\\n 1. 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s;\\r\\n}\\r\\n<\\/pre>\\r\\n<\\/p>\\r\\n\\r\\n\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n HASH_DEL(users, user); \\r\\n}\\r\\n<\\/pre>\\r\\n<\\/p>\"],\"csharp\":[\"C#\",\"\\/debug:pdbonly<\\/code>)\\u3002<\\/p>\"],\"javascript\":[\"JavaScript\",\"Node.js 16.13.2<\\/code><\\/p>\\r\\n\\r\\n--harmony<\\/code> \\u6807\\u8bb0\\u6765\\u5f00\\u542f \\u65b0\\u7248ES6\\u7279\\u6027<\\/a>\\u3002<\\/p>\\r\\n\\r\\nRuby 3.1<\\/code>\\u6267\\u884c<\\/p>\\r\\n\\r\\nSwift 5.5.2<\\/code><\\/p>\\r\\n\\r\\nGo 1.17<\\/code><\\/p>\\r\\n\\r\\nPython 3.10<\\/code><\\/p>\\r\\n\\r\\nScala 2.13<\\/code><\\/p>\"],\"kotlin\":[\"Kotlin\",\"Kotlin 1.3.10<\\/code><\\/p>\"],\"rust\":[\"Rust\",\"rust 1.58.1<\\/code><\\/p>\\r\\n\\r\\nPHP 8.1<\\/code>.<\\/p>\\r\\n\\r\\n