Let $W(n,k)$ be the number of ways in which $n$ can be written as the product of $k$ distinct positive integers.

For example, $W(144,4)=7$. There are $7$ ways in which $144$ can be written as a product of $4$ distinct positive integers:

• $144=1\times 2\times 4\times 18$
• $144=1\times 2\times 8\times 9$
• $144=1\times 2\times 3\times 24$
• $144=1\times 2\times 6\times 12$
• $144=1\times 3\times 4\times 12$
• $144=1\times 3\times 6\times 8$
• $144=2\times 3\times 4\times 6$

Note that permutations of the integers themselves are not considered distinct.

Furthermore, $W(100!,10)$ modulo $1000000007=287549200$.

Find $W(10000!,30)$ modulo $1000000007$.