Brute Force Fails!! (Code It Or Not)\text{Brute Force Fails!! }\color{gold}{\text{(Code It Or Not)}}

Algebra Level 5

Recurrent sequence {ar}\{a_r\} is such that a1=7273682a_1 = 7273682 and ar=rar+(r1)a_r = ra_{\lfloor \sqrt{r} \rfloor} + (r - 1) for r>1r > 1.

Find the value of:

(r=110101ar)mod1000000007\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.


Difficulty: \dagger \dagger \dagger \dagger \dagger

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