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 $\mathrm{lcm}$, of a list is the smallest natural number divisible by each entry of the list.
Examples: $\mathrm{lcm}(2,6,4)=12$, $\mathrm{lcm}(10,6,15,6)=30$ and $\mathrm{lcm}(11)=11$.

Let $f(G,L,N)$ be the number of lists of size $N$ with $gcd\ge G$ and $\mathrm{lcm}\le L$. For example:

$f(10,100,1)=91$.
$f(10,100,2)=327$.
$f(10,100,3)=1135$.
$f(10,100,1000)mod{101}^4=3286053$.

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