<p>A conveyor belt has packages that must be shipped from one port to another within <code>days</code> days.</p>

<p>The <code>i<sup>th</sup></code> package on the conveyor belt has a weight of <code>weights[i]</code>. Each day, we load the ship with packages on the conveyor belt (in the order given by <code>weights</code>). We may not load more weight than the maximum weight capacity of the ship.</p>

<p>Return the least weight capacity of the ship that will result in all the packages on the conveyor belt being shipped within <code>days</code> days.</p>

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

<pre>
<strong>Input:</strong> weights = [1,2,3,4,5,6,7,8,9,10], days = 5
<strong>Output:</strong> 15
<strong>Explanation:</strong> A ship capacity of 15 is the minimum to ship all the packages in 5 days like this:
1st day: 1, 2, 3, 4, 5
2nd day: 6, 7
3rd day: 8
4th day: 9
5th day: 10

Note that the cargo must be shipped in the order given, so using a ship of capacity 14 and splitting the packages into parts like (2, 3, 4, 5), (1, 6, 7), (8), (9), (10) is not allowed.
</pre>

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

<pre>
<strong>Input:</strong> weights = [3,2,2,4,1,4], days = 3
<strong>Output:</strong> 6
<strong>Explanation:</strong> A ship capacity of 6 is the minimum to ship all the packages in 3 days like this:
1st day: 3, 2
2nd day: 2, 4
3rd day: 1, 4
</pre>

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

<pre>
<strong>Input:</strong> weights = [1,2,3,1,1], days = 4
<strong>Output:</strong> 3
<strong>Explanation:</strong>
1st day: 1
2nd day: 2
3rd day: 3
4th day: 1, 1
</pre>

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

<ul>
	<li><code>1 &lt;= days &lt;= weights.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= weights[i] &lt;= 500</code></li>
</ul>

from typing import List

class Solution:
    def shipWithinDays(self, weights: List[int], days: int) -> int:
        def canShipWithCapacity(capacity):
            total = 0
            days_counter = 1  # Start with the first day
            for weight in weights:
                if total + weight > capacity:

                    days_counter += 1
                    total = 0
                total += weight
            return days_counter <= days

        # Binary search between max(weights) and sum(weights)
        left, right = max(weights), sum(weights)
        while left < right:
            mid = (left + right) // 2
            if canShipWithCapacity(mid):
                right = mid  # Try a smaller capacity
            else:
                left = mid + 1  # Increase the capacity
        
        return left

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