On day $1$, exactly one person discovers a secret.

Each person who learns the secret will begin sharing it with one new person every day, but only after a waiting period of delay days from when they first discovered it. Additionally, each person completely forgets the secret forget days after discovering it. Once a person has forgotten the secret (on the day of forgetting and all subsequent days), they can no longer share it.

Given an integer n, determine how many people know the secret at the end of day n. Since the result can be very large, return it modulo $10^9 + 7$.

Note: A person who discovered the secret on day d can share it starting from day d + delay through day d + forget - 1 (inclusive), and they forget it on day d + forget.

Constraints:

• $2 \leq$ n $\leq 1000$

• $1 \leq$ delay $<$ forget $\leq$ n

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.