--description--

The binomial coefficient $\displaystyle\binom{{10}^{18}}{{10}^9}$ is a number with more than 9 billion ($9 × {10}^9$) digits.

Let $M(n, k, m)$ denote the binomial coefficient $\displaystyle\binom{n}{k}$ modulo $m$.

Calculate $\sum M({10}^{18}, {10}^9, p \times q \times r)$ for $1000 < p < q < r < 5000$ and $p$, $q$, $r$ prime.

--hints--

hugeBinomialCoefficient() should return 162619462356610300.

assert.strictEqual(hugeBinomialCoefficient(), 162619462356610300);

--seed--

--seed-contents--

function hugeBinomialCoefficient() {

  return true;
}

hugeBinomialCoefficient();

--solutions--

// solution required