# Problem 495: Writing n as the product of k distinct positive integers
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.