<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> result;
        for (int i = max(0, k - (int)nums2.size()); i <= min(k, (int)nums1.size()); ++i) {
            result = max(result, merge(maxArray(nums1, i), maxArray(nums2, k - i)));
        }
        return result;
    }
private:
    vector<int> maxArray(vector<int>& nums, int k) {
        vector<int> result(k);
        int n = nums.size(), j = 0;
        for (int i = 0; i < n; ++i) {
            while (j > 0 && j + n - i > k && result[j - 1] < nums[i]) --j;
            if (j < k) result[j++] = nums[i];
        }
        return result;
    }
    vector<int> merge(vector<int> nums1, vector<int> nums2) {
        vector<int> result;
        while (!nums1.empty() || !nums2.empty()) {
            if (nums1 > nums2) {
                result.push_back(nums1[0]);
                nums1.erase(nums1.begin());
            } else {
                result.push_back(nums2[0]);
                nums2.erase(nums2.begin());
            }
        }
        return result;
    }
};
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