<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>

from sortedcontainers import SortedList
class Solution:
    def maxNumber(self, left: List[int], right: List[int], k: int) -> List[int]:
        result = [0 for _ in range(k)]

        def get_best(arr, to_take):
            stack = []

            for i in range(len(arr)):
                elements_here_and_to_right = len(arr) - i
                while len(stack) + elements_here_and_to_right > to_take and (stack and arr[i] > stack[-1]):
                    stack.pop()
                    
                if len(stack) < to_take:
                    stack.append(arr[i])
            
            return stack
        
        def compare(alpha, beta, a, b):
            if a >= len(alpha):
                return False
            
            if b >= len(beta):
                return True
            if alpha[a] > beta[b]:
                return True
            
            if alpha[a] < beta[b]:
                return False
            
            return compare(alpha, beta, a + 1, b + 1)

        def merge(alpha, beta):
            merged = []
            a = 0
            b = 0

            while a < len(alpha) or b < len(beta):
                if compare(alpha, beta, a, b):
                    merged.append(alpha[a])
                    a += 1
                else:
                    merged.append(beta[b])
                    b += 1

            return merged

        for to_take_from_left in range(max(0, k - len(right)), min(k, len(left)) + 1):
            to_take_from_right = k - to_take_from_left

            candidate = merge(get_best(left, to_take_from_left), get_best(right, to_take_from_right))            

            if compare(candidate, result, 0,0):
                result = candidate
  
        return result

        
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