<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 
{
private:
    long long mod = 1e9 + 7;
    unordered_map<int, int> idx;
    //vector<vector<long long>> dp;
    long long dp[100002][2];
    
public:
    int maxSum(vector<int>& nums1, vector<int>& nums2) 
    {        
        int m = nums1.size();
        int n = nums2.size();                
        for(int i = 0; i < n; ++i) idx[nums2[i]] = i;
        
        int len = max(m, n);
        //dp.resize(len + 1, vector<long long>(2, -1));
        memset(dp, 0, sizeof(dp));
        
        int i = 0;
        int j = 0;
        while(true)
        {            
            for(; i < m; ++i)
            {
                if(idx.find(nums1[i]) != idx.end()) break;
                dp[i + 1][0] += dp[i][0] + nums1[i];
            }
            
            int maxJ = (i == m) ? n : idx[nums1[i]];
            for(; j < maxJ; ++j)
            {
                dp[j + 1][1] += dp[j][1] + nums2[j];
            }
            
            if(i >= m && j >= n) break;
            
            dp[i + 1][0] = max(dp[i][0], dp[j][1]) + nums1[i];
            dp[j + 1][1] = max(dp[i][0], dp[j][1]) + nums1[i];
            
            ++i;
            ++j;
        }
        
        // for(int i = 0; i <= m; ++i) cout<<dp[i][0]<<" "; cout<<endl;
        // for(int j = 0; j <= n; ++j) cout<<dp[j][1]<<" "; cout<<endl;
        
        return max(dp[m][0], dp[n][1]) % mod;
    }    
};
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