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.
\r\n
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 。
\n\n
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
\n\n
提示：
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