<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:
    
    unordered_map<int,int>mp,mp2;
    int mod=1e9+7;
    long long helper(vector<int>& nums1, vector<int>& nums2,int turn,int j,vector<vector<long long>>&dp){
        if(turn==0 && j==nums1.size())return 0;
        if(turn==1 && j==nums2.size())return 0;
        if(dp[turn][j]!=-1)return dp[turn][j];

        if(turn==0){
           int v=nums1[j];
           long long p1=v+helper(nums1,nums2,turn,j+1,dp);
           long long p2=0;
           if(mp2.find(v)!=mp2.end()){
              p2=v+helper(nums1,nums2,!turn,mp2[v]+1,dp);
           }
           return dp[turn][j]=(max(p1,p2)); 
        }
        else{
           int v=nums2[j]; 
           long long p1=helper(nums1,nums2,turn,j+1,dp)+v;
           long long p2=0;
           if(mp.find(v)!=mp.end()){
              p2=v+helper(nums1,nums2,!turn,mp[v]+1,dp); 
           }
           return dp[turn][j]=(max(p1,p2));  
        }
    } 
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        int maxi=max(nums1.size(),nums2.size());
        for(int i=0;i<nums1.size();i++)mp[nums1[i]]=i;
        for(int i=0;i<nums2.size();i++)mp2[nums2[i]]=i;
        vector<vector<long long>>dp(2,vector<long long>(maxi+1,-1));  
        long long v1= helper(nums1,nums2,0,0,dp);
        long long v2=helper(nums1,nums2,1,0,dp); 
        long long res=max(v1,v2);
        int ans =res%mod;
        ans+=mod;
        ans=ans%mod;
        return ans;
    }
};
121994