<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:
    // Find the greatest subsequence of length k from array a
    vector<int> greaterSubsequence(vector<int>& a, int k) {
        vector<int> ans;
        int n = a.size();
        for (int i = 0; i < n; i++) {
            while (!ans.empty() && ans.back() < a[i] &&
                   (k - ans.size()) < (n - i)) {
                ans.pop_back();
            }
            if(ans.size()<k) ans.push_back(a[i]);
        }
        // Resize the result to size k
        // ans.resize(k);
        return ans;
    }

    // Merge two subsequences into one, ensuring the result has a length of k
    void pop_front(std::vector<int>& v) {
        if (v.size() > 0)
            v.erase(v.begin());
    }
    vector<int> merge(vector<int> p1, vector<int> p2, int k) {
        vector<int> temp;
        for (int j = 0; j < k; j++) {
            vector<int> temp2 = max(p1, p2);
            int fr = temp2.front();
            if (p1 > p2)
                pop_front(p1);
            else
                pop_front(p2);
            temp.push_back(fr);
        }
        return temp;
    }

    // Main function to find the maximum number
    vector<int> maxNumber(vector<int>& a, vector<int>& b, int k) {
        vector<int> ans(k, 0);
        for (int i = 0; i <= k; i++) {
            if (i > a.size() || k - i > b.size())
                continue;
            vector<int> aa = greaterSubsequence(a, i);
            vector<int> bb = greaterSubsequence(b, k - i);
            vector<int> cc = merge(aa, bb, k);

            ans = max(ans, cc);
        }
        return ans;
    }
};
215682