You are given three integers l, r, and k.

Consider all valid sequences of length k where each digit is an integer chosen from the inclusive range $[$l$, $`r`$]$. Each sequence forms a $k$ digit number where positions represent powers of $10$.

Return the sum of all such numbers. Since the answer may be large, return it modulo $10^9 + 7$.

Note: Numbers with leading zeros are evaluated by their standard numeric value.

Constraints:

• $0 \le$ l $\le$ r $\le 9$

• $1 \le$ k $\le 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.