**IPO** Suppose LeetCode will start its **IPO** soon. In order to sell a good price of its shares to Venture Capital, LeetCode would like to work on some projects to increase its capital before the **IPO**. Since it has limited resources, it can only finish at most `k`

distinct projects before the **IPO**. Help LeetCode design the best way to maximize its total capital after finishing at most `k`

distinct projects.

You are given `n`

projects where the `i`

project has a pure profit ^{th}`profits[i]`

and a minimum capital of `capital[i]`

is needed to start it.

Initially, you have `w`

capital. When you finish a project, you will obtain its pure profit and the profit will be added to your total capital.

Pick a list of **at most** `k`

distinct projects from given projects to **maximize your final capital**, and return *the final maximized capital*.

The answer is guaranteed to fit in a 32-bit signed integer.

**Example 1:**

Input:k = 2, w = 0, profits = [1,2,3], capital = [0,1,1]Output:4Explanation:Since your initial capital is 0, you can only start the project indexed 0. After finishing it you will obtain profit 1 and your capital becomes 1. With capital 1, you can either start the project indexed 1 or the project indexed 2. Since you can choose at most 2 projects, you need to finish the project indexed 2 to get the maximum capital. Therefore, output the final maximized capital, which is 0 + 1 + 3 = 4.

**Example 2:**

Input:k = 3, w = 0, profits = [1,2,3], capital = [0,1,2]Output:6

**Constraints:**

`1 <= k <= 10`

^{5}`0 <= w <= 10`

^{9}`n == profits.length`

`n == capital.length`

`1 <= n <= 10`

^{5}`0 <= profits[i] <= 10`

^{4}`0 <= capital[i] <= 10`

^{9}

### IPO Solutions

✅**Time:** O(n)

✅**Space:** O(n)

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**Python**

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