## Writing n as the product of k distinct positive integers

### Problem 495

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 = 1×2×4×18
- 144 = 1×2×8×9
- 144 = 1×2×3×24
- 144 = 1×2×6×12
- 144 = 1×3×4×12
- 144 = 1×3×6×8
- 144 = 2×3×4×6

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

Furthermore, `W`(100!,10) modulo 1 000 000 007 = 287549200.

Find `W`(10000!,30) modulo 1 000 000 007.