Water Bottles II

Medium

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Hint

You are given two integers numBottles and numExchange.

• numBottles represents the number of full water bottles that you initially have.
• In one operation, you can perform one of the following operations:

1. Drink any number of full water bottles turning them into empty bottles.
2. Exchange numExchange empty bottles with one full water bottle. Then, increase numExchange by one.

⚠️ Note: You cannot exchange multiple batches of empty bottles for the same value of numExchange.
For example, if numBottles == 3 and numExchange == 1, you cannot exchange 3 empty water bottles for 3 full bottles.

Return the maximum number of water bottles you can drink.

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Example 1

Input:

numBottles = 13, numExchange = 6

Output:

15

Step-by-step table (Full / Empty / numExchange / cumulative drunk):

Step	Action	Full (after)	Empty (after)	numExchange (used → new / or current)	Drunk (cumulative)
0	Start	13	0	6	0
1	Drink 13	0	13	6	13
2	Exchange (use 6)	1	7	6 → 7	13
3	Exchange (use 7)	2	0	7 → 8	13
4	Drink 2	0	2	8	15

Final answer: 15

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Example 2

Input:

numBottles = 10, numExchange = 3

Output:

13

Step-by-step table (Full / Empty / numExchange / cumulative drunk):

Step	Action	Full (after)	Empty (after)	numExchange (used → new / or current)	Drunk (cumulative)
0	Start	10	0	3	0
1	Drink 10	0	10	3	10
2	Exchange (use 3)	1	7	3 → 4	10
3	Exchange (use 4)	2	3	4 → 5	10
4	Drink 2	0	5	5	12
5	Exchange (use 5)	1	0	5 → 6	12
6	Drink 1	0	1	6	13

Final answer: 13

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Constraints

• 1 <= numBottles <= 100
• 1 <= numExchange <= 100