<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 {
public:
    vector<int> getGrtSubseq(vector<int>& nums, int requiredLength) {
        vector<int> ans;
        int n = nums.size();

        for(int i = 0 ; i < n ; i++) {
            while(ans.size() > 0 && ans.back() < nums[i] && ((requiredLength - ans.size()) < (n - i))) {
                ans.pop_back();
            }
            if(ans.size() < requiredLength) {
                ans.push_back(nums[i]);
            }
        }

        return ans;
    }

    vector<int> maxNumber(vector<int>& nums1, vector<int>& nums2, int k) {
        vector<int> num(k, 0);

        for(int i = max(0, k - (int)nums2.size()); i <= min(k, (int)nums1.size()); i++) {
            vector<int> left = getGrtSubseq(nums1, i);
            vector<int> right = getGrtSubseq(nums2, k - i);
            vector<int> curr;
            int l = 0, r = 0;

            // Merging the two subsequences
            while(l < left.size() && r < right.size()) {
                if(left[l] > right[r]) {
                    curr.push_back(left[l]);
                    l++;
                } else if(left[l] < right[r]) {
                    curr.push_back(right[r]);
                    r++;
                } else {
                    // Compare the remaining parts of left and right for lexicographical order
                    if(vector<int>(left.begin() + l, left.end()) > vector<int>(right.begin() + r, right.end())) {
                        curr.push_back(left[l]);
                        l++;
                    } else {
                        curr.push_back(right[r]);
                        r++;
                    }
                }
            }

            while(l < left.size()) curr.push_back(left[l++]);
            while(r < right.size()) curr.push_back(right[r++]);

            if(curr > num) num = curr;
        }

        return num;
    }
};
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