<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 n1,n2;
    int mod=1e9+7;
    long long int dp[100001][2];
    long long int solve(int i,int turn,vector<int>& num1, vector<int>& num2,map<int,int> &m1,map<int,int> &m2)
    {
        if(i>=n1 && turn==1)
        return 0;

        if(i>=n2 && turn==0)
        return 0;

        if(dp[i][turn]!=-1)
        return dp[i][turn];
              
        int num=(turn)?num1[i]:num2[i];

        long long int pick=0;
        long long int notP=num+solve(i+1,turn,num1,num2,m1,m2);

        if(turn && m2.find(num1[i])!=m2.end())
        {
            int idx=m2[num1[i]]+1;
            pick=num1[i]+solve(idx,!turn,num1,num2,m1,m2);
        }

        if(turn==0 && m1.find(num2[i])!=m1.end())
        {
            int idx=m1[num2[i]]+1;
            pick=num2[i]+solve(idx,!turn,num1,num2,m1,m2);
        }    
        
        return dp[i][turn]=(max(pick,notP));
    }

    int maxSum(vector<int>& num1, vector<int>& num2) {
        n1=num1.size();n2=num2.size();
        map<int,int> m1,m2;
        for(int i=0;i<n1;i++)
        m1[num1[i]]=i;

        for(int i=0;i<n2;i++)
        m2[num2[i]]=i;

        memset(dp,-1,sizeof dp);

        long long int a=(solve(0,1,num1,num2,m1,m2))%mod;
        long long int b=(solve(0,0,num1,num2,m1,m2))%mod;
        
        return (int)(max(a,b))%mod;
    }
};
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