--description--

For fixed integers $a$, $b$, $c$, define the crazy function $F(n)$ as follows:

$$\begin{align} & F(n) = n - c \;\text{ for all } n > b \\ & F(n) = F(a + F(a + F(a + F(a + n)))) \;\text{ for all } n ≤ b. \end{align}$$

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

For example, if $a = 50$, $b = 2000$ and $c = 40$, then $F(0) = 3240$ and $F(2000) = 2040$. Also, $S(50, 2000, 40) = 5\,204\,240$.

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

--hints--

crazyFunction() should return 291504964.

assert.strictEqual(crazyFunction(), 291504964);

--seed--

--seed-contents--

function crazyFunction() {

  return true;
}

crazyFunction();

--solutions--

// solution required