You are given two positive integers n and limit.

Determine the total number of ways to distribute n candies among $3$ children such that no child receives more than limit candies.

Constraints:

• $1 \leq$ n $\leq 10^8$

• $1 \leq$ limit $\leq 10^8$

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.