<p>You are given two arrays of integers <code>nums1</code> and <code><font face="monospace">nums2</font></code>, possibly of different lengths. The values in the arrays are between <code>1</code> and <code>6</code>, inclusive.</p>

<p>In one operation, you can change any integer&#39;s value in <strong>any </strong>of the arrays to <strong>any</strong> value between <code>1</code> and <code>6</code>, inclusive.</p>

<p>Return <em>the minimum number of operations required to make the sum of values in </em><code>nums1</code><em> equal to the sum of values in </em><code>nums2</code><em>.</em> Return <code>-1</code>​​​​​ if it is not possible to make the sum of the two arrays equal.</p>

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

<pre>
<strong>Input:</strong> nums1 = [1,2,3,4,5,6], nums2 = [1,1,2,2,2,2]
<strong>Output:</strong> 3
<strong>Explanation:</strong> You can make the sums of nums1 and nums2 equal with 3 operations. All indices are 0-indexed.
- Change nums2[0] to 6. nums1 = [1,2,3,4,5,6], nums2 = [<u><strong>6</strong></u>,1,2,2,2,2].
- Change nums1[5] to 1. nums1 = [1,2,3,4,5,<strong><u>1</u></strong>], nums2 = [6,1,2,2,2,2].
- Change nums1[2] to 2. nums1 = [1,2,<strong><u>2</u></strong>,4,5,1], nums2 = [6,1,2,2,2,2].
</pre>

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

<pre>
<strong>Input:</strong> nums1 = [1,1,1,1,1,1,1], nums2 = [6]
<strong>Output:</strong> -1
<strong>Explanation:</strong> There is no way to decrease the sum of nums1 or to increase the sum of nums2 to make them equal.
</pre>

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

<pre>
<strong>Input:</strong> nums1 = [6,6], nums2 = [1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> You can make the sums of nums1 and nums2 equal with 3 operations. All indices are 0-indexed. 
- Change nums1[0] to 2. nums1 = [<strong><u>2</u></strong>,6], nums2 = [1].
- Change nums1[1] to 2. nums1 = [2,<strong><u>2</u></strong>], nums2 = [1].
- Change nums2[0] to 4. nums1 = [2,2], nums2 = [<strong><u>4</u></strong>].
</pre>

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

<ul>
	<li><code>1 &lt;= nums1.length, nums2.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums1[i], nums2[i] &lt;= 6</code></li>
</ul>

class Solution:
    def minOperations(self, nums1: List[int], nums2: List[int]) -> int:
        """
        1. keep sum(nums1) <= sum(nums2), i.e. swap if not
        2. calculate capacity as max diff by raising nums1 and lowering nums2
        3. if diff between nums1 and nums2 <= capacity: then optimally allocate the operation in sorted distance list
        4. otherwise, no solution, return -1
        """
        # swap input to keep sum(nums1) <= sum(nums2)
        if sum(nums1) - sum(nums2) < 0:
            nums1, nums2 = nums2, nums1
        elif sum(nums1) - sum(nums2) == 0:
            return 0
        count = 0 
        diff = sum(nums1) - sum(nums2)   
        # capacity: diff upperbound achieved by raising nums1 and lowering nums2
        d12 = sorted([n - 1 for n in nums1] + [6 - n for n in nums2], reverse=True)

        # if diff <= upper bound, then bridge gap in an optimal way; otherwise no solution
        if diff <= sum(d12):
            # ordered distance list by mixing nums1 to 1 and nums2 to 6
            for d in d12:
                diff -= d
                count += 1
                if diff <= 0:
                    return count
        
        return -1

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