An investor is looking to maximize their capital by undertaking a set of profitable projects. Due to limited time and resources, they can complete at most k distinct projects.

There are $n$ available projects. Each project i has:

• A profit of profits[i] earned upon completion.

• A minimum capital requirement of capital[i] needed to start the project.

The investor starts with an initial capital of c. After completing a project, its profit is immediately added to the investor's current capital.

The goal is to choose up to k different projects in a way that maximizes the investor’s final capital. Return the maximum capital achievable after completing these projects.

It is guaranteed that the answer fits within a 32-bit signed integer.

Constraints:

• $1 \leq$ k $\leq 10^3$

• $0 \leq$ c $\leq$ $10^9$

• $n==$ profits.length

• $n==$ capitals.length

• $1 \leq n \leq 10^3$

• $0 \leq$profits[i] $\leq 10^4$

• $0 \leq$ capitals[i] $\leq 10^9$

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.