<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>

class Solution:
    def maxNumber(self, nums1: List[int], nums2: List[int], k: int) -> List[int]:
        def prep(nums, k):
            drop = len(nums) - k
            out = []
            for num in nums:
                while drop and out and out[-1] < num:
                    out.pop()
                    drop -= 1
                out.append(num)
            return out[:k]
        
        def merge(a, b):
            return [max(a, b).pop(0) for _ in a+b]
        
        return max(merge(prep(nums1, i), prep(nums2, k-i)) for i in range(k+1) if i <= len(nums1) and k-i <= len(nums2))
        
        """
        def merge(n1, n2):
            res = []
            while (n1 or n2) :
                if n1>n2:
                    res.append(n1[0])
                    n1 = n1[1:]
                else:
                    res.append(n2[0])
                    n2 = n2[1:]
            return res
        
        def findmax(nums, length):
            l = []
            maxpop = len(nums)-length
            for i in range(len(nums)):
                while maxpop>0 and len(l) and nums[i]>l[-1]:
                    l.pop()
                    maxpop -= 1
                l.append(nums[i])
            return l[:length]
        
        n1 = len(nums1)
        n2 = len(nums2)
        res = [0]*k
        for i in range(k+1):
            j = k-i
            if i>n1 or j>n2:    continue
            l1 = findmax(nums1, i)
            l2 = findmax(nums2, j)
            res = max(res, merge(l1,l2))
        return res """
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