<p>You are given two integer arrays <code>nums1</code> and <code>nums2</code> of lengths <code>m</code> and <code>n</code> respectively. <code>nums1</code> and <code>nums2</code> represent the digits of two numbers. You are also given an integer <code>k</code>.</p>

<p>Create the maximum number of length <code>k &lt;= m + n</code> from digits of the two numbers. The relative order of the digits from the same array must be preserved.</p>

<p>Return an array of the <code>k</code> digits representing the answer.</p>

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

<pre>
<strong>Input:</strong> nums1 = [3,4,6,5], nums2 = [9,1,2,5,8,3], k = 5
<strong>Output:</strong> [9,8,6,5,3]
</pre>

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

<pre>
<strong>Input:</strong> nums1 = [6,7], nums2 = [6,0,4], k = 5
<strong>Output:</strong> [6,7,6,0,4]
</pre>

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

<pre>
<strong>Input:</strong> nums1 = [3,9], nums2 = [8,9], k = 3
<strong>Output:</strong> [9,8,9]
</pre>

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

<ul>
	<li><code>m == nums1.length</code></li>
	<li><code>n == nums2.length</code></li>
	<li><code>1 &lt;= m, n &lt;= 500</code></li>
	<li><code>0 &lt;= nums1[i], nums2[i] &lt;= 9</code></li>
	<li><code>1 &lt;= k &lt;= m + n</code></li>
</ul>

def bestMinus1(nums: List[int]):
    ln = len(nums)
    for i in range(ln - 1):
        if nums[i] < nums[i+1]:
            del nums[i]
            break
    if ln == len(nums):
        nums.pop()

def produceBests(nums: List[int], shortest, longest):
    result = []
    while True:
        if len(nums) <= longest:
            result.append(nums.copy())
        if len(nums) == shortest:
            break
        bestMinus1(nums)
    result.reverse()
    return result

def getBestMix(nums1: List[int], nums2: List[int]) -> List[int]:
    if not nums1:
        return nums2
    if not nums2:
        # nums1 is being reused.
        return nums1.copy()
    if nums1 >= nums2:
        return [nums1[0]] + getBestMix(nums1[1:], nums2)
    return [nums2[0]] + getBestMix(nums1, nums2[1:])

class Solution:
    def maxNumber(self, nums1: List[int], nums2: List[int], k: int) -> List[int]:
        l1 = len(nums1)
        l2 = len(nums2)

        minFrom2 = max(0, k - l1)
        maxFrom2 = min(k, l2)
        bests2 = produceBests(nums2, minFrom2, maxFrom2)
        
        minFrom1 = k - maxFrom2
        maxFrom1 = k - minFrom2

        while len(nums1) > maxFrom1:
            bestMinus1(nums1)

        bestCandidate = []
        while True:
            from1 = len(nums1)
            from2 = k - from1
            candidate = getBestMix(nums1, bests2[from2 - minFrom2])
            if bestCandidate < candidate:
                bestCandidate = candidate
            if len(nums1) <= minFrom1:
                break
            bestMinus1(nums1)
        return bestCandidate
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