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`