<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> max_seq_from_vec(vector<int>& num, int k) {
        vector<int> res;
        if (k == 0) return res;
        int n = num.size();
        for(int i = 0; i < n; ++i) {
            while(!res.empty() && res.back() < num[i] && res.size()-1 + n-i >= k) {
                res.pop_back();
            }
            if (res.size() < k) {
                res.push_back(num[i]);
            }
        }
        return res;
    }
    
    bool compare(vector<int>& v1, int i, vector<int>& v2, int j) {
        while(i < v1.size() and j < v2.size() and v1[i] == v2[j]) {
            i ++; j ++;
        }
        if (j == v2.size()) return true; // v1 > v2
        if (i == v1.size()) return false;
        return v1[i] > v2[j];
    }
    vector<int> merge(vector<int>& a, vector<int>& b) {
        vector<int> res;
        int i = 0, j = 0;
        while(i < a.size() && j < b.size()) {
            if (compare(a, i, b, j)) {
                res.push_back(a[i]); i++;
            } else {
                res.push_back(b[j]); j++;
            }
        }
        while(i < a.size()) {
            res.push_back(a[i]); i++;
        }
        while(j < b.size()) {
            res.push_back(b[j]); j++;
        }
        return res;
    }
    vector<int> maxNumber(vector<int>& nums1, vector<int>& nums2, int k) {
        int n1 = nums1.size();
        int n2 = nums2.size();

        vector<int> ans(k, -1);
        for(int i = 0; i <= k; ++i) {
            auto v1 = max_seq_from_vec(nums1, i);
            auto v2 = max_seq_from_vec(nums2, k-i);
            if (v1.size() + v2.size() != k) continue;

            auto merged = merge(v1, v2);
            if (!compare(ans, 0, merged, 0))
                ans = merged;
        }
        return ans;
    }
};
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