Crazy Function

For fixed integers $a, b, c$, define the crazy function $F(n)$ as follows: $F(n) = n - c$ for all $n > b$ $F(n) = F(a + F(a + F(a + F(a + n))))$ for all $n ≤ b$

Also, define $S(a, b, c) =\sum_{n=0}^b F(n)$.

For example, if $a = 50, b = 2000$ and $c = 40$, then $F(0) = 3240$ and $F(2000) = 2040$. Also, $S(50, 2000, 40) = 5204240$.

Find the last $9$ digits of $S(21^7, 7^{21}, 12^7)$.