<p>You are given an integer array <code>bloomDay</code>, an integer <code>m</code> and an integer <code>k</code>.</p>

<p>You want to make <code>m</code> bouquets. To make a bouquet, you need to use <code>k</code> <strong>adjacent flowers</strong> from the garden.</p>

<p>The garden consists of <code>n</code> flowers, the <code>i<sup>th</sup></code> flower will bloom in the <code>bloomDay[i]</code> and then can be used in <strong>exactly one</strong> bouquet.</p>

<p>Return <em>the minimum number of days you need to wait to be able to make </em><code>m</code><em> bouquets from the garden</em>. If it is impossible to make m bouquets return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> bloomDay = [1,10,3,10,2], m = 3, k = 1
<strong>Output:</strong> 3
<strong>Explanation:</strong> Let us see what happened in the first three days. x means flower bloomed and _ means flower did not bloom in the garden.
We need 3 bouquets each should contain 1 flower.
After day 1: [x, _, _, _, _]   // we can only make one bouquet.
After day 2: [x, _, _, _, x]   // we can only make two bouquets.
After day 3: [x, _, x, _, x]   // we can make 3 bouquets. The answer is 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> bloomDay = [1,10,3,10,2], m = 3, k = 2
<strong>Output:</strong> -1
<strong>Explanation:</strong> We need 3 bouquets each has 2 flowers, that means we need 6 flowers. We only have 5 flowers so it is impossible to get the needed bouquets and we return -1.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> bloomDay = [7,7,7,7,12,7,7], m = 2, k = 3
<strong>Output:</strong> 12
<strong>Explanation:</strong> We need 2 bouquets each should have 3 flowers.
Here is the garden after the 7 and 12 days:
After day 7: [x, x, x, x, _, x, x]
We can make one bouquet of the first three flowers that bloomed. We cannot make another bouquet from the last three flowers that bloomed because they are not adjacent.
After day 12: [x, x, x, x, x, x, x]
It is obvious that we can make two bouquets in different ways.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>bloomDay.length == n</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= bloomDay[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= m &lt;= 10<sup>6</sup></code></li>
	<li><code>1 &lt;= k &lt;= n</code></li>
</ul>

from typing import List

class Solution:
    def minDays(self, bloomDay: List[int], m: int, k: int) -> int:
        # Total number of flowers required for m bouquets
        total_flowers_required = m * k
        
        # If we don't have enough flowers, it's impossible to make m bouquets
        if len(bloomDay) < total_flowers_required:
            return -1

        # Binary search boundaries
        l = min(bloomDay)
        r = max(bloomDay)

        # Helper function to count how many bouquets can be made in 'md' days
        def make_groups(md):
            groups = 0
            flowers = 0

            # Iterate through each bloomDay and check if we can form bouquets
            for bloom in bloomDay:
                if bloom <= md:
                    flowers += 1  # Flower has bloomed within 'md' days
                    if flowers == k:  # We can form a bouquet
                        groups += 1
                        flowers = 0  # Reset for the next bouquet
                else:
                    flowers = 0  # Can't use this flower, reset the count

            return groups

        # Binary search
        while l <= r:
            md = (l + r) // 2
            groups = make_groups(md)  # Number of groups (bouquets) we can form in 'md' days

            if groups < m:
                # Not enough bouquets, we need more days
                l = md + 1
            else:
                # We can form enough bouquets, try fewer days
                r = md - 1

        return l if l <= max(bloomDay) else -1

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