--description--

A list of size $n$ is a sequence of $n$ natural numbers. Examples are (2, 4, 6), (2, 6, 4), (10, 6, 15, 6), and (11).

The greatest common divisor, or $gcd$, of a list is the largest natural number that divides all entries of the list. Examples: $gcd(2, 6, 4) = 2$, $gcd(10, 6, 15, 6) = 1$ and $gcd(11) = 11$.

The least common multiple, or $lcm$, of a list is the smallest natural number divisible by each entry of the list. Examples: $lcm(2, 6, 4) = 12$, $lcm(10, 6, 15, 6) = 30$ and $lcm(11) = 11$.

Let $f(G, L, N)$ be the number of lists of size $N$ with $gcd ≥ G$ and $lcm ≤ L$. For example:

$$\begin{align} & f(10, 100, 1) = 91 \\ & f(10, 100, 2) = 327 \\ & f(10, 100, 3) = 1135 \\ & f(10, 100, 1000)\bmod {101}^4 = 3\,286\,053 \end{align}$$

Find $f({10}^6, {10}^{12}, {10}^{18})\bmod {101}^4$.

--hints--

leastGreatestAndGreatestLeast() should return 84664213.

assert.strictEqual(leastGreatestAndGreatestLeast(), 84664213);

--seed--

--seed-contents--

function leastGreatestAndGreatestLeast() {

  return true;
}

leastGreatestAndGreatestLeast();

--solutions--

// solution required