Words with Gaps (noch nicht übersetzt)
Problem 873
Let $W(p,q,r)$ be the number of words that can be formed using the letter A $p$ times, the letter B $q$ times and the letter C $r$ times with the condition that every A is separated from every B by at least two Cs. For example, CACACCBB is a valid word for $W(2,2,4)$ but ACBCACBC is not.
You are given $W(2,2,4)=32$ and $W(4,4,44)=13908607644$.
Find $W(10^6,10^7,10^8)$. Give your answer modulo $1\,000\,000\,007$.