<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 
{
private:
    vector<int>maxnum(vector<int>nums,int k)
    {
        int n = nums.size();
        vector<int>st;
        for(int i=0;i<n;i++)
        {
            
            while(!st.empty() && st.back()<nums[i] && (n-i)+(st.size()-1)>=k)
            {
                st.pop_back();
            }

            if(st.size()<k)
            {
                st.push_back(nums[i]);
            }
        
        }

        return st;
    }

    vector<int> merge(vector<int>arr1,vector<int>arr2)
    {
        vector<int>res;
        // int i=0;

        while(!arr1.empty() || !arr2.empty())
        {
            if(arr1>arr2)
            {
                res.push_back(arr1.front());
                arr1.erase(arr1.begin());
            }
            else
            {
                res.push_back(arr2.front());
                arr2.erase(arr2.begin());
            }
            // i++;
        }
    
        return res;
    }
public:
    vector<int> maxNumber(vector<int>& nums1, vector<int>& nums2, int k) 
    {
        int n=nums1.size();
        int m=nums2.size();
        
        vector<int>maxi;
        
        for(int i=0; i<=k && i<=n; i++)
        {
            if(k-i>m) continue;
            
            vector<int>arr1 = maxnum(nums1,i);
            vector<int>arr2 = maxnum(nums2,k-i);
            
            vector<int>merged = merge(arr1,arr2);
            if(merged>maxi)
                maxi = merged;  
        }

        return maxi;
    }
};
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