You start with numBottles full water bottles and drink them one by one. After drinking a bottle, it becomes an empty bottle. Whenever you have at least numExchange empty bottles, you may trade exactly numExchange empty bottles for 1 new full bottle. This exchange can be performed any number of times as long as you have enough empty bottles.

Return the maximum total number of bottles you can drink.

Constraints:

• $1 \leq$ numBottles $\leq 100$

• $2 \leq$ numExchange $\leq 100$

Input: numBottles = 1-int, numExchange = 2-int
Output: 1-int
Explanation: You drink the 1 full bottle and get 1 empty bottle. Since 1 < 2, you can’t exchange, so the total drunk is 1.

Input: numBottles = 10-int, numExchange = 11-int
Output: 10-int
Explanation: After drinking all 10 bottles, you have 10 empty bottles. Since 10 < 11, no exchange is possible, so the total drunk remains 10.

Input: numBottles = 7-int, numExchange = 7-int
Output: 8-int
Explanation: Drinking 7 bottles gives 7 empties (total = 7). Exchanging the 7 empties for 1 full bottle and drinking it makes the total 8. Now you have 1 empty, and 1 < 7, so you stop.

Input: numBottles = 100-int, numExchange = 2-int
Output: 199-int
Explanation: With an exchange rate of 2 empties for 1 full bottle, every 2 empties yields another drink. Starting from 100 bottles, you can keep exchanging until only 1 empty remains, resulting in 199 total bottles drunk.

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