<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]:
        output = []

        def get_monotonic_stack(nums, upper_bound):
            stack = []

            n = len(nums)
            for idx, num in enumerate(nums):
                remain = n - idx
                while stack and stack[-1] < num and len(stack) + remain > upper_bound:
                    stack.pop()

                if len(stack) < upper_bound:
                    stack.append(num)
            
            return stack

        def merge(stack1, stack2):
            output = []

            l, r = 0, 0

            m, n = len(stack1), len(stack2)

            while l < m and r < n:
                left = stack1[l:]
                right = stack2[r:]

                if left > right:
                    output.append(stack1[l])
                    l += 1
                else:
                    output.append(stack2[r])
                    r += 1
            
            if r == n:
                output.extend(stack1[l:])
            
            if l == m:
                output.extend(stack2[r:])
            
            return output

        answer = []

        for i in range(max(0, k - len(nums2)), min(len(nums1), k) + 1):
            stack1 = get_monotonic_stack(nums1, i)
            stack2 = get_monotonic_stack(nums2, k - i)

            merged = merge(stack1, stack2)

            answer = max(answer, merged)
        
        return answer
16500