A program concatenated all positive integers of an array into a single string s with no separators.

Every integer in the original array met the following conditions:

• The value was between $1$ and k inclusive.

• The value did not contain any leading zeros.

Given the string s and the integer k, return the total number of valid arrays that could have formed s. Since the answer may be large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ s.length $\leq 10^5$

• s consists of only digits and does not contain leading zeros.

• $1 \leq$ k $\leq 10^9$

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.