Recurrent sequence $\{a_r\}$ is such that $a_1 = 7273682$ and $a_r = ra_{\lfloor \sqrt{r} \rfloor} + (r - 1)$ for $r > 1$.

Find the value of:

$\left(\sum_{r = 1}^{10^{10} - 1}a_r\right) \bmod 1000000007$

**Notation:** $\lfloor . \rfloor$ denotes the floor function.

Try using a code

All of my problems are **original**.