You are given two integers, numBottles and numExchange.

Initially, you have numBottles full water bottles. In one operation, you can perform one of the following actions:

• Drink any number of full water bottles, turning each into an empty water bottle.

• Exchange numExchange empty water bottles for $1$ full water bottle, and then increase the value of numExchange by $1$.

Return the maximum number of water bottles you can drink.

Note: Each exchange operation consumes numExchange empty bottles and immediately increments numExchange by $1$. You cannot perform multiple exchanges simultaneously with the same numExchange value.

Constraints:

• $1 \leq$ numBottles $\leq 100$

• $1 \leq$ numExchange $\leq 100$

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.