Eccoci.

In this problem $\oplus$ is used to represent the bitwise exclusive or of two numbers.
Starting with blank paper repeatedly do the following:

1. Write down the smallest positive integer $a$ which is currently not on the paper;
2. Find the smallest positive integer $b$ such that neither $b$ nor $(a\oplus b)$ is currently on the paper. Then write down both $b$ and $(a\oplus b)$.

After the first round $\{1,2,3\}$ will be written on the paper. In the second round $a=4$ and because $(4\oplus 5)$, $(4\oplus 6)$ and $(4\oplus 7)$ are all already written $b$ must be $8$.

After $n$ rounds there will be $3n$ numbers on the paper. Their sum is denoted by $M(n)$.
For example, $M(10)=642$ and $M(1000)=5432148$.

Find $M({10}^{18})$. Give your answer modulo $1000000007$.