experience-23

--description--

For a positive integer $k$, define $d(k)$ as the sum of the digits of $k$ in its usual decimal representation. Thus $d(42) = 4 + 2 = 6$.

For a positive integer $n$, define $S(n)$ as the number of positive integers $k < {10}^n$ with the following properties:

• $k$ is divisible by 23 and,
• $d(k) = 23$.

You are given that $S(9) = 263\,626$ and $S(42) = 6\,377\,168\,878\,570\,056$.

Find $S({11}^{12})$ and give your answer $\bmod {10}^9$.

--hints--

experience23() should return 789184709.

assert.strictEqual(experience23(), 789184709);

--seed--

--seed-contents--

function experience23() {

  return true;
}

experience23();

--solutions--

// solution required