Divisors

A natural number $a$ is called a divisor of a natural number $b$ if b = ac for some natural number $c$. For example, the divisors of $6$ are $1$, $2$, $3$, and $6$. Two numbers are called coprime if they have no common divisors other than $1$. For example, $16$ and $27$ are coprime, but $18$ and $24$ are not.

We call a set of $k$ numbers (a_1, a_2, \ldots, a_k) normal if the following conditions are satisfied:

1. each number a_i is a divisor of $n$;

2. a_1 < a_2 < \ldots < a_k;

3. for every $i$ from $1$ to k-1, the numbers a_i and a_{i+1} are coprime;

4. the product a_1 a_2 \ldots a_k does not exceed $n$.

For example, the set (2, 9, 10) is a normal set of $3$ divisors of $360$.

Write a program that, given $n$ and $k$, determines the number of normal sets of $k$ divisors of $n$.