<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:
    const int mod = 1e9 + 7;
    long long int help(int index , int path , unordered_map<int,int>&path1 , unordered_map<int,int>&path2 , vector<int>&nums1 , vector<int>&nums2 , vector<vector<long long int>>&dp)
    {
        if(path == 1)
        {
            if(index >= nums1.size() )
            {
                return 0;
            }
        }
        else if(path == 2 )
        {
            if(index >= nums2.size())
            {
                return 0;
            }
        }
        
        if(dp[index][path]!=-1)
        {
            return dp[index][path];
        }
        
        if(path == 1)
        {
            long long int op1 = nums1[index] + help(index+1 , 1 , path1 , path2 , nums1 , nums2 , dp);
            long long int op2 = 0;
            if(path2.find( nums1[index] ) != path2.end())
            {
                op2 = nums1[index] + help( path2[nums1[index]]+1 , 2 , path1 , path2 , nums1 , nums2 , dp);
            }
            return dp[index][path] = max(op1,op2);
        }
        else
        {
            long long int op1 = nums2[index] + help(index+1 , 2 , path1 , path2 , nums1 , nums2 , dp);
            long long int op2 = 0;
            if(path1.find( nums2[index] ) != path1.end())
            {
                op2 = nums2[index] + help( path1[nums2[index]]+1 , 1 , path1 , path2 , nums1 , nums2 , dp);
            }
            return dp[index][path] = max(op1,op2);
        }
    }
    
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        unordered_map<int,int>path1;
        unordered_map<int,int>path2;
        
        for(int i=0;i<nums1.size();i++)
        {
            path1[nums1[i]] = i;
        }
        
        for(int i=0;i<nums2.size();i++)
        {
            path2[nums2[i]] = i;
        }
         
        int maxLen = max(nums1.size(),nums2.size());
        vector<vector<long long int>>dp(maxLen+1,vector<long long int>(2+1,-1));
        
        long long int res1 = (help(0,1,path1,path2,nums1,nums2,dp))%mod;
        long long int res2 = (help(0,2,path1,path2,nums1,nums2,dp))%mod;
        
        return max(res1,res2)%mod;
    }
};
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