<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:
    map<int,pair<int,int>>mp;
    
    long long mod= 1e9+7;
    long long func(int ind,bool f,vector<int>& nums1, vector<int>& nums2,vector<vector<long long>>&dp){
        vector<int> &nums=f?nums2:nums1;
        // if(f==0){
        //     nums=nums1;
        // }
        // else{
        //     nums=nums2;
        // }
        if(ind==nums.size()) return 0; 
        if(dp[ind][f]!=-1) return dp[ind][f];
        long long sum=0;
        sum= nums[ind]+func(ind+1,f,nums1,nums2,dp);
        if(mp.find(nums[ind])!=mp.end()){
            int ind1= mp[nums[ind]].first;
            int ind2= mp[nums[ind]].second;
            if(f==0){
                
                sum=max(sum,nums[ind]+func(ind2+1,1,nums1,nums2,dp));
            }
            else{
                
                sum=max(sum,nums[ind]+func(ind1+1,0,nums1,nums2,dp));
            }
        }
        
        return dp[ind][f]= sum;
    }
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        int n= nums1.size();
        int m= nums2.size();
        
        int i=0,j=0;
        while(i<n && j<m){
            if(nums1[i]==nums2[j]){
                mp[nums1[i]]={i,j};
                i++;
                j++;
            }
            else if(nums1[i]<nums2[j]) i++;
            else j++;
        }
        vector<vector<long long>>dp(max(n,m),vector<long long>(2,-1));
        return max(func(0,0,nums1,nums2,dp),func(0,1,nums1,nums2,dp))%mod;

    }
};
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