<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:
    int n ,m ;
    map<int,int>mp1;
    map<int,int>mp2;
   long long dp[100010][2];
   const int mod = 1e9+7 ;

    long long  rec(int level,int f,vector<int>&nums1,vector<int>&nums2){
          
          if(f == 0 && level == nums1.size())return 0 ;
          if(f == 1 && level == nums2.size())return 0 ;

          if(dp[level][f] != -1)return dp[level][f];
         long long ans = 0 ;
         if(f == 0){
              ans = max(ans,nums1[level] + rec(level+1,0,nums1,nums2) );
              if(mp2.find(nums1[level]) != mp2.end()){
                 ans = max(ans,nums1[level] + rec(mp2[nums1[level]]+1,1,nums1,nums2) );
              }
         }
         else{
              ans = max(ans,nums2[level]+ rec(level+1,1,nums1,nums2) );
              if(mp1.find(nums2[level]) != mp1.end() ){
                 ans = max(ans,nums2[level] + rec(mp1[nums2[level]]+1,0,nums1,nums2) );
              }
         }
         return dp[level][f] = ans ;
    }
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        memset(dp,-1,sizeof(dp));
        mp1.clear();
        mp2.clear();

        for(int i =0 ; i<nums1.size(); i++){
            mp1[nums1[i]] = i ;
        }
        for(int i =0 ; i<nums2.size(); i++){
            mp2[nums2[i]] = i ;
        }
        long long int ans = max(rec(0,0,nums1,nums2)%mod,rec(0,1,nums1,nums2)%mod);
        return ans ;
    }
};
105876