public class Solution
extends Object
1808 - Maximize Number of Nice Divisors\.
Hard
You are given a positive integer `primeFactors`. You are asked to construct a positive integer `n` that satisfies the following conditions:
* The number of prime factors of `n` (not necessarily distinct) is **at most** `primeFactors`.
* The number of nice divisors of `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`.
**Example 1:**
**Input:** primeFactors = 5
**Output:** 6
**Explanation:** 200 is a valid value of n. It has 5 prime factors: [2,2,2,5,5], and it has 6 nice divisors: [10,20,40,50,100,200]. There is not other value of n that has at most 5 prime factors and more nice divisors.
**Example 2:**
**Input:** primeFactors = 8
**Output:** 18
**Constraints:**
* 1 <= primeFactors <= 109