<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]:
        # take  max k from the first list and take k from the second list
        def greedySelection(j, n1):
            # if j is too big cut into down to length if first
            j = min(j , len(n1))
            drop = len(n1) - j ## how many you are allowed to drop
            s1 = []
            for i in range(0, len(n1)):
                curr = n1[i]
                
                while drop and s1 and s1[-1] < curr:
                    drop -= 1
                    s1.pop()
                    continue
                s1.append(curr)
            return s1[:j]


        def merge(n1, n2):
            n1, n2 = deque(n1) , deque(n2)
            ret = []
            while n1 or n2:
                if n1 > n2:  # Compare lexicographically remaining parts of both lists
                    ret.append(n1.popleft())
                else:
                    ret.append(n2.popleft())
            return ret
        best = []
        for i in range(0, k + 1):
            if i == 9:
                print("debug")
       
            res = merge( greedySelection(k-i, nums1) , greedySelection(i, nums2) )
            if len(res) > len(best):
                best = res
            elif len(res) == len(best) and res > best:
                best = res
        return best


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