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What is the best way to generate first N primes? (not primes up to N but first N primes)

We are given a list of N integers and another positive integer K. We need to compute the number of ways in which the product P of the
given N integers can be expressed as a product of K positive integers (not
necessarily distinct). The order of the factors in the expression is not
important. For example, 1 x 2 x 3 and 2 x 3 x 1 are not counted as different
ways of expressing 6 as a product of three integers.

Input Format
The first line contains two space-separated integers, N and K
The next line contains N-space separated integers

Output
One line containing the number of ways in which the product of the N
integers can be expressed as a product of K positive integers


Example:
Input
2 3
4 16
Output
7
Explanation
The product is 64. This can be expressed as a product of three integers in
the following ways:
1 x 1 x 64
1 x 2 x 32
1 x 4 x 16
1 x 8 x 8
2 x 2 x 16
2 x 4 x 8
4 x 4 x 4

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