<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:

   bool isALarger(int i,int j,vector<int> a,vector<int> &b){
         
        while(i<a.size()&&j<b.size()){
            if(a[i]>b[j])return true;
            else if(b[j]>a[i])return false;
            else{
                i++;
                j++;
            }
        }

        if(j<b.size())return false;
        return true;
   }

    bool compare(vector<int> &a,vector<int> &b){
        if(a.size()==0)return true;

        for(int i=0;i<a.size();i++){
            if(a[i]>b[i])return false;
            else if(b[i]>a[i])return true;
        }
        return false;
    }

    vector<int> find(int cnt,vector<int> &a){

        vector<int> ans;
        stack<int> st;

        for(int i=0;i<a.size();i++){
             
             while(!st.empty()&&st.size()+(a.size()-i-1)>=cnt&&st.top()<a[i])
                st.pop();

             if(st.size()<cnt)st.push(a[i]);   
        }

        while(!st.empty()){
            ans.push_back(st.top());
            st.pop();
        }

        reverse(ans.begin(),ans.end());

        return ans;
    }

    vector<int> maxNumber(vector<int>& nums1, vector<int>& nums2, int k) {

        vector<int> ans;

        for(int x=max(0,k-(int)nums2.size());x<=min(k,(int)nums1.size());x++){
          
            vector<int> a=find(x,nums1);
            vector<int> b=find(k-x,nums2);

            vector<int> temp(k);

            int i=0,j=0;
            int curr=0;

            while(i<a.size()&&j<b.size()){
                 
                 if(a[i]>b[j]){
                    temp[curr++]=a[i++];
                 }
                 else if(b[j]>a[i])temp[curr++]=b[j++];
                 else if(isALarger(i,j,a,b))temp[curr++]=a[i++];
                 else temp[curr++]=b[j++];
            }
            while(i<a.size()){
                temp[curr++]=a[i++];
            }
            while(j<b.size()){
                temp[curr++]=b[j++];
            }

            if(compare(ans,temp))ans=temp;
        }

        return ans;
    }
};
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