1808. Maximize Number of Nice Divisors

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.

class Solution {
    const int MOD = 1e9 + 7;
    long fastPow(long n, long p) {
        long res = 1L;
        while(p) {
            if(p & 1)
                res = res * n % MOD;
            n = n * n % MOD;
            p>>=1;
        }
        return res;
    }
public:
    int maxNiceDivisors(int primeFactors) {
        if(primeFactors < 4)
            return primeFactors;
        int prefix = primeFactors % 3 == 0 ? 3 : primeFactors % 3 == 1 ? 4 : 6;
        return prefix * fastPow(3, primeFactors / 3 - 1) % MOD;
    }
};