<p>You have <code>n</code> packages that you are trying to place in boxes, <strong>one package in each box</strong>. There are <code>m</code> suppliers that each produce boxes of <strong>different sizes</strong> (with infinite supply). A package can be placed in a box if the size of the package is <strong>less than or equal to</strong> the size of the box.</p>

<p>The package sizes are given as an integer array <code>packages</code>, where <code>packages[i]</code> is the <strong>size</strong> of the <code>i<sup>th</sup></code> package. The suppliers are given as a 2D integer array <code>boxes</code>, where <code>boxes[j]</code> is an array of <strong>box sizes</strong> that the <code>j<sup>th</sup></code> supplier produces.</p>

<p>You want to choose a <strong>single supplier</strong> and use boxes from them such that the <strong>total wasted space </strong>is <strong>minimized</strong>. For each package in a box, we define the space <strong>wasted</strong> to be <code>size of the box - size of the package</code>. The <strong>total wasted space</strong> is the sum of the space wasted in <strong>all</strong> the boxes.</p>

<ul>
	<li>For example, if you have to fit packages with sizes <code>[2,3,5]</code> and the supplier offers boxes of sizes <code>[4,8]</code>, you can fit the packages of size-<code>2</code> and size-<code>3</code> into two boxes of size-<code>4</code> and the package with size-<code>5</code> into a box of size-<code>8</code>. This would result in a waste of <code>(4-2) + (4-3) + (8-5) = 6</code>.</li>
</ul>

<p>Return <em>the <strong>minimum total wasted space</strong> by choosing the box supplier <strong>optimally</strong>, or </em><code>-1</code> <i>if it is <strong>impossible</strong> to fit all the packages inside boxes. </i>Since the answer may be <strong>large</strong>, return it <strong>modulo </strong><code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> packages = [2,3,5], boxes = [[4,8],[2,8]]
<strong>Output:</strong> 6
<strong>Explanation</strong>: It is optimal to choose the first supplier, using two size-4 boxes and one size-8 box.
The total waste is (4-2) + (4-3) + (8-5) = 6.
</pre>

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

<pre>
<strong>Input:</strong> packages = [2,3,5], boxes = [[1,4],[2,3],[3,4]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> There is no box that the package of size 5 can fit in.
</pre>

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

<pre>
<strong>Input:</strong> packages = [3,5,8,10,11,12], boxes = [[12],[11,9],[10,5,14]]
<strong>Output:</strong> 9
<strong>Explanation:</strong> It is optimal to choose the third supplier, using two size-5 boxes, two size-10 boxes, and two size-14 boxes.
The total waste is (5-3) + (5-5) + (10-8) + (10-10) + (14-11) + (14-12) = 9.
</pre>

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

<ul>
	<li><code>n == packages.length</code></li>
	<li><code>m == boxes.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= m &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= packages[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= boxes[j].length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= boxes[j][k] &lt;= 10<sup>5</sup></code></li>
	<li><code>sum(boxes[j].length) &lt;= 10<sup>5</sup></code></li>
	<li>The elements in <code>boxes[j]</code> are <strong>distinct</strong>.</li>
</ul>

from typing import List
from bisect import bisect_right
import math

class Solution:
    def minWastedSpace(self, packages: List[int], boxes: List[List[int]]) -> int:
        # Sort the packages to facilitate binary search
        packages.sort()
        
        # Initialize the minimum wasted space to infinity
        ans = math.inf
        
        # Iterate over each supplier's box sizes
        for box in boxes:
            # Sort the box sizes for the current supplier
            box.sort()
            
            # Check if the largest package can fit in the largest box
            if packages[-1] <= box[-1]:
                kk = val = 0
                
                # Calculate the total wasted space for this supplier
                for x in box:
                    # Find the position where the current box size can fit the packages
                    k = bisect_right(packages, x)
                    
                    # Calculate the waste for the current box size
                    val += (k - kk) * x
                    kk = k
                
                # Update the minimum wasted space
                ans = min(ans, val)
        
        # Calculate the total size of all packages
        total_package_size = sum(packages)
        
        # Return the minimum wasted space modulo 1_000_000_007, or -1 if no valid supplier
        return (ans - total_package_size) % 1_000_000_007 if ans < math.inf else -1
1098