Writing down the numbers which have a digit sum of 10 in ascending order, we get: $19,28,37,46,55,64,73,82,91,109,118,\dots$

Let $f(n,m)$ be the $m^{\text{th}}$ occurrence of the digit sum $n$. For example, $f(10,1)=19$, $f(10,10)=109$ and $f(10,100)=1423$.

Let ${\displaystyle S(k)=\sum _{n=1}^{k}f(n^3,n^4)}$. For example $S(3)=7128$ and $S(10)\equiv 32287064\mathrm{mod}1000000007$.

Find $S(10000)$ modulo $1000000007$.