<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> maxNumber(vector<int>& nums1, vector<int>& nums2, int k) {
        vector<int> ans;
        const int n1 = nums1.size();
        const int n2 = nums2.size();
        for (int i = max(0, k - n2); i <= min(k, n1); ++i)
            ans = max(ans, maxNumber(maxNumber(nums1, i), 
                                     maxNumber(nums2, k - i)));
        return ans;
    }
private:    
    vector<int> maxNumber(const vector<int>& nums, int k) {
        vector<int> ans(k);                
        int j = 0;
        for (int i = 0; i < nums.size(); ++i) {
            while (j > 0 && nums[i] > ans[j - 1] 
                   && nums.size() - i > k - j) --j;
            if (j < k) ans[j++] = nums[i];
        }
        return ans;
    }
    
    vector<int> maxNumber(const vector<int>& nums1, const vector<int>& nums2) {
        vector<int> ans(nums1.size() + nums2.size());
        auto s1 = nums1.cbegin();
        auto e1 = nums1.cend();
        auto s2 = nums2.cbegin();
        auto e2 = nums2.cend();        
        int index = 0;
        while (s1 != e1 || s2 != e2)
            ans[index++] = 
              lexicographical_compare(s1, e1, s2, e2) ? *s2++ : *s1++;
        return ans;
    }
};
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