<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>solve(int k,vector<int>nums)
    {
        int n=nums.size();
        if(k>n) return {};
        int toLeave=n-k;
        vector<int>res;
        res.push_back(nums[0]);
        for(int i=1;i<n;i++)
        {
            while(!res.empty() && nums[i]>res.back() && toLeave>0)
            {
                res.pop_back();
                toLeave--;
            }
            res.push_back(nums[i]);
        }
        //to remove the lowest elements if possible 
        while(toLeave)
        {
            res.pop_back();
            toLeave--;
        }
        return res;
    }

    void merge(vector<int>&ans,vector<int>nums1,vector<int>nums2)
    {
        int n1=nums1.size();
        int n2=nums2.size();
        int i=0,j=0;
        while(i<n1 && j<n2)
        {
            if(nums1[i]==nums2[j])
            {
                int tempi=i;
                int tempj=j;
                while(tempi<n1 && tempj<n2 && nums1[tempi]==nums2[tempj])
                {
                    tempi++;
                    tempj++;
                }
                if(tempi==n1)
                {
                    ans.push_back(nums2[j]);
                    j++;
                }
                else if(tempj==n2)
                {
                    ans.push_back(nums1[i]);
                    i++;
                }
                else if(nums1[tempi]>nums2[tempj])
                {
                    ans.push_back(nums1[i]);
                    i++;
                }
                else
                {
                    ans.push_back(nums2[j]);
                    j++;
                }
            }
            else if(nums1[i]>nums2[j])
            {
                ans.push_back(nums1[i]);
                i++;
            }
            else
            {
                ans.push_back(nums2[j]);
                j++;
            }
        }
        while(i<n1)
        {
            ans.push_back(nums1[i]);i++;
        }
        while(j<n2)
        {
            ans.push_back(nums2[j]);j++;
        }
    }


    vector<int> maxNumber(vector<int>& nums1, vector<int>& nums2, int k) {
        vector<int>ans;
        for(int i=0;i<=k;i++)
        {
            vector<int>temp1=solve(i,nums1);
            vector<int>temp2=solve(k-i,nums2);
            vector<int>temp;
            merge(temp,temp1,temp2);
            if(temp.size()==k) ans=max(ans,temp);
        }
        return ans;
    }
};
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