• 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

Solution: Math

Time complexity: O(logn)
Space complexity: O(1)

// Author: Huahua
class Solution {
public:
  int maxNiceDivisors(int n) {
    constexpr int kMod = 1e9 + 7;
    auto powm = [](long base, int exp) {
      long ans = 1;
      while (exp) {
        if (exp & 1) ans = (ans * base) % kMod;
        base = (base * base) % kMod;
        exp >>= 1;
      }
      return ans;
    };
    
    if (n <= 3) return n;
    switch (n % 3) {
      case 0: return powm(3, n / 3);
      case 1: return (powm(3, n / 3 - 1) * 4) % kMod;
      case 2: return (powm(3, n / 3) * 2) % kMod;
    }
    return -1;
  }
};

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