<p>You are given two <strong>sorted</strong> arrays of distinct integers <code>nums1</code> and <code>nums2</code>.</p>

<p>A <strong>valid<strong><em> </em></strong>path</strong> is defined as follows:</p>

<ul>
	<li>Choose array <code>nums1</code> or <code>nums2</code> to traverse (from index-0).</li>
	<li>Traverse the current array from left to right.</li>
	<li>If you are reading any value that is present in <code>nums1</code> and <code>nums2</code> you are allowed to change your path to the other array. (Only one repeated value is considered in the valid path).</li>
</ul>

<p>The <strong>score</strong> is defined as the sum of unique values in a valid path.</p>

<p>Return <em>the maximum score you can obtain of all possible <strong>valid paths</strong></em>. Since the answer may be too large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/07/16/sample_1_1893.png" style="width: 500px; height: 151px;" />
<pre>
<strong>Input:</strong> nums1 = [2,4,5,8,10], nums2 = [4,6,8,9]
<strong>Output:</strong> 30
<strong>Explanation:</strong> Valid paths:
[2,4,5,8,10], [2,4,5,8,9], [2,4,6,8,9], [2,4,6,8,10],  (starting from nums1)
[4,6,8,9], [4,5,8,10], [4,5,8,9], [4,6,8,10]    (starting from nums2)
The maximum is obtained with the path in green <strong>[2,4,6,8,10]</strong>.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [1,3,5,7,9], nums2 = [3,5,100]
<strong>Output:</strong> 109
<strong>Explanation:</strong> Maximum sum is obtained with the path <strong>[1,3,5,100]</strong>.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [1,2,3,4,5], nums2 = [6,7,8,9,10]
<strong>Output:</strong> 40
<strong>Explanation:</strong> There are no common elements between nums1 and nums2.
Maximum sum is obtained with the path [6,7,8,9,10].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums1.length, nums2.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums1[i], nums2[i] &lt;= 10<sup>7</sup></code></li>
	<li><code>nums1</code> and <code>nums2</code> are strictly increasing.</li>
</ul>

class Solution {
public:
    long long int t[100001][3];
    const int mod=1e9+7;
    long long int solve(unordered_map <int,int>&path1,unordered_map <int,int>&path2,int path,int index,vector<int>&nums1,vector<int>&nums2){
         //base case
         if(path==1){
            if(index>=path1.size())return 0;
         }else if(path==2){
            if(index>=path2.size())return 0;
         }
         
         if(t[index][path]!=-1){
            return t[index][path];
         }

         if(path==1){
           long long int sum1=nums1[index]+solve(path1,path2,1,index+1,nums1,nums2);
           long long int sum2=0;
           if(path2.find(nums1[index])!=path2.end()){
            sum2=nums1[index]+solve(path1,path2,2,path2[nums1[index]]+1,nums1,nums2);
           }
           return t[index][path]=max(sum1,sum2);
         }else{
         long long int sum1=nums2[index]+solve(path1,path2,2,index+1,nums1,nums2);
           long long int sum2=0;
           if(path1.find(nums2[index])!=path1.end()){
            sum2=nums2[index]+solve(path1,path2,1,path1[nums2[index]]+1,nums1,nums2);
           }
           return t[index][path]=max(sum1,sum2);
         }   
    };
    
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        unordered_map <int,int>path1;

        unordered_map <int,int>path2;
        memset(t,-1,sizeof(t));
        int k=0;
        for(int i:nums1){
            path1[i]=k;
            k++;

        }
        k=0;
        for(int i:nums2){
            path2[i]=k;
            k++;
        }

        long long int ans1=solve(path1,path2,1,0,nums1,nums2);
        long long int ans2=solve(path1,path2,2,0,nums1,nums2);


        return max(ans1,ans2)%mod;


    }
};
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