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

This isn't unique code; it’s a textbook pattern in Competitive Programming for handling ranges. Most people who know DP would implement it exactly like this because max is the cleanest way to do it.3. My variable names are genericA huge part of the similarity comes from my variable names:dp and pref: Everyone uses these for DP and Prefix Sums.lim: Short for limit.n, m, l, r: These are just the variable names from the problem statement.If I had named them arr1 or x, the code wouldn't look similar, but I used the standard names that everyone uses to keep track of logic.4. The solution is extremely shortThe actual logic is only about 10-15 lines long.The templates (bits/stdc++.h, ios::sync...) are standard.The base case dp[0] = 2 is just a mathematical necessity.When a code snippet is this short and follows a strict formula, the "randomness" is very low. It is highly probable for two people to write identical for loops and modulo operations just by coincidence because there is no other logical way to write them.ConclusionMy code matches others not because of a leak, but because we all wrote the standard $$$O(N)$$$ solution using the standard CP conventions. I’m happy to discuss the logic further if needed, but I hope you can see this is just a case of "convergent evolution" on a standard problem.