You are given an integer array bloomDay, where bloomDay[i] is the day the ith flower blooms.

You want to make exactly m bouquets. Each bouquet must consist of exactly k flowers that are adjacent in the array, and each flower can be used in at most one bouquet.

Return the minimum day such that it is possible to make m bouquets by that day. If it is impossible to make m bouquets, return $-1$.

Note: A flower is considered available on day d if bloomDay[i] \leq d.

Constraints:

• bloomDay.length == n

• $1 \leq$ n $\leq 10^5$

• $1 \leq$ bloomDay[i] $\leq 10^9$

• $1 \leq$ m $\leq 10^6$

• $1 \leq$ k $\leq$ n

Input: bloomDay = [1, 10, 3, 10, 2]-List[int], m = 3-int, k = 1-int
Output: 3-int
Explanation: With k = 1, each bouquet needs just one flower. By day 3, the flowers with bloom days 1, 3, and 2 are available (3 flowers total), so we can make m = 3 bouquets. Day 2 only gives 2 flowers, which is not enough.

Input: bloomDay = [1, 10, 3, 10, 2]-List[int], m = 3-int, k = 2-int
Output: -1-int
Explanation: Each bouquet needs 2 adjacent flowers, so we would need at least m * k = 6 flowers total, but n = 5. It’s impossible regardless of the day.

Input: bloomDay = [7, 7, 7, 7, 12, 7, 7]-List[int], m = 2-int, k = 3-int
Output: 12-int
Explanation: By day 7, the available flowers form groups [7,7,7,7] (length 4) and [7,7] (length 2), yielding floor(4/3) = 1 bouquet total, which is not enough. By day 12, all flowers are available as one contiguous group of length 7, yielding floor(7/3) = 2 bouquets, which meets m = 2 and is the minimum day.

Input: bloomDay = [1, 2, 4, 9, 3, 4, 1]-List[int], m = 2-int, k = 2-int
Output: 4-int
Explanation: By day 3, the available pattern is [1,2] (one bouquet), then a break at 4,9, then [3], then a break at 4, then [1], giving only 1 bouquet. By day 4, the available flowers are [1,2,4] (length 3, 1 bouquet) and [3,4,1] (length 3, 1 bouquet), for a total of 2 bouquets, so day 4 works and is minimal.

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.