<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 {
    long long dp[100002][2];
    const int mod = 1e9+7;
    long long helper(int i , int curr , vector<int> &nums1 , vector<int> &nums2 , map<int,int> &mp , map<int,int> &mp1)
    {
           if(i==nums1.size() and curr==0)
           {
              return 0;
           }
           if(i==nums2.size() and curr==1)
           {
              return 0;
           }
           if(dp[i][curr]!=-1)
           {
              return dp[i][curr];
           }
           long long take =0;
           long long n_take=0;
           int curr1 ;
          
           long long score =0;
           if(curr==0)
           {
              score=nums1[i];
           }
           if(curr==1)
           {
              score=nums2[i];
           }
           take = (score + helper(i+1,curr , nums1,nums2,mp,mp1));
           if(i<nums2.size() and mp.find(nums2[i])!=mp.end()   and curr==1)
           {
              
               n_take = (score+helper(mp[nums2[i]]+1,0,  nums1 , nums2,mp,mp1));
           }
           if(i<nums1.size() and mp1.find(nums1[i])!=mp1.end()  and curr==0)
           {
              
               n_take = (score+helper(mp1[nums1[i]]+1 ,1,  nums1 , nums2,mp,mp1));
           }
           return dp[i][curr]=max(take,n_take);


    }
public:
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        map<int,int> mp ;
        map<int,int> mp1 ;
        memset(dp,-1,sizeof(dp));
        for(int i =0 ; i<nums1.size() ; i++)
        {
             mp[nums1[i]]=i ;
        }
        for(int i =0 ; i<nums2.size() ; i++)
        {
             mp1[nums2[i]]=i;
        }
        return max(helper(0,0,nums1,nums2,mp,mp1),helper(0,1,nums1,nums2,mp,mp1))%mod;
    }
};
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