## Crazy Function

### Problem 340

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 $S(a, b, c) = \sum \limits_{n = 0}^{b} {F(n)}$.

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}).