Jack has three plates in front of him. The giant has $N$ beans that he distributes to the three plates. All the beans look the same, but one of them is a magic bean. Jack doesn't know which one it is, but the giant knows.

Jack can ask the giant questions of the form: "Does this subset of the beans contain the magic bean?" In each question Jack may choose any subset of beans from a single plate, and the giant will respond truthfully.

If the three plates contain $a$, $b$ and $c$ beans respectively, we let $h(a,b,c)$ be the minimal number of questions Jack needs to ask in order to guarantee he locates the magic bean. For example, $h(1,2,3)=3$ and $h(2,3,3)=4$.

Let $H(N)$ be the sum of $h(a,b,c)$ over all triples of non-negative integers $a$, $b$, $c$ with $1\le a+b+c\le N$.
You are given: $H(6)=203$ and $H(20)=7718$.

A repunit, $R_n$, is a number made up with $n$ digits all '1'. For example, $R_3=111$ and $H(R_3)=1634144$.

Find $H(R_{19})$. Give your answer modulo $1000000007$.