I am writing this to address the plagiarism flag regarding my submission [351044555] for problem 2170E. I understand that my code shares significant similarities with several other users. However, I want to clarify that this code was written independently.

The "coincidence" is a result of the problem requiring a highly specific, standard mathematical approach (Linear DP with Prefix Sum optimization) which leaves very little room for implementation variation. Below are the specific points explaining why this convergence occurred naturally.

1. Standard Mathematical Recurrence

The problem reduces to finding the number of valid binary strings where the last block satisfies specific constraints. The recurrence relation is standard for this type of problem:

To solve this in $$$O(N)$$$ (which is required given $$$N \le 3 \cdot 10^5$$$), one must use prefix sums. My code calculates:

cur = pref[i-1] - pref[L-1]

This is the direct translation of the math formula. Any optimal solution must write this exact line of logic. There is no other efficient way to express this.

2. Constraint Propagation Logic

The way I handled the input constraints is the standard "Right-endpoint maximization" technique:

cpp
lim[r] = max(lim[r], l); // Store tightest constraint ending at r
// ... later ...
lim[i] = max(lim[i], lim[i-1]); // Propagate the constraint forward