<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 {
    int MOD = 1e9+7;
    long long solve(int i, bool b, vector<vector<int>>&v, vector<unordered_map<int,int>>&mp, vector<vector<long long>>&dp){
        if(i==v[b].size()) return 0;
        if(dp[i][b]!=LLONG_MIN) return dp[i][b];
        long long ans = v[b][i];
        long long next = solve(i+1,b,v,mp,dp);
        if(next!=LLONG_MIN) ans+= next;
        if(mp[1-b].find(v[b][i])!=mp[1-b].end()){
            ans = max(ans,v[b][i]+solve(mp[1-b][v[b][i]]+1,1-b,v,mp,dp));
        }
        return dp[i][b] = ans;        
    }
public:
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        int n1 = nums1.size();
        int n2 = nums2.size();
        vector<vector<long long>> dp(max(n1,n2),vector<long  long>(2,LLONG_MIN));
        vector<vector<int>> v = {nums1,nums2};
        vector<unordered_map<int,int>> mp(2,unordered_map<int,int>());
        for(int i=0;i<n1;i++){
            mp[0][nums1[i]] = i;
        }
        for(int i=0;i<n2;i++){
            mp[1][nums2[i]] = i;
        }
        long long ans = max(solve(0,0,v,mp,dp),solve(0,1,v,mp,dp));
        return ans%MOD;
    }
};
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