<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:
    const int mod = 1e9 + 7;
    int n1, n2;
    unordered_map<int,int> idx1, idx2;
    vector<vector<long long>> dp;
    long long helper(vector<int>& nums1, vector<int>& nums2, int curr, int type) {
        if (((type == 0) and (curr >= n1)) or ((type == 1) and (curr >= n2)))
            return 0;
        if (dp[curr][type] != -1)   
            return dp[curr][type];
        
        long long res = 0;
        res = fmax(res, 
            ((type == 0) ? nums1[curr] : nums2[curr]) + 
            helper(nums1, nums2, curr + 1, type));

        if (((type == 0) and idx2.count(nums1[curr])) or ((type == 1) and idx1.count(nums2[curr]))) 
            res = fmax(res, 
                ((type == 0) ? nums1[curr] : nums2[curr]) + 
                helper(nums1, nums2, ((type == 0) ? idx2[nums1[curr]] : idx1[nums2[curr]]) + 1, 1 - type));
        return dp[curr][type] = res;
    }

    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        n1 = nums1.size();
        n2 = nums2.size();

        for (int i = 0; i < n1; i++)
            idx1[nums1[i]] = i;
        for (int i = 0; i < n2; i++)
            idx2[nums2[i]] = i;
    
        dp.resize(max(n1,n2), vector<long long> (2, -1));
        long long ans = fmax(
            helper(nums1,nums2, 0, 0),
            helper(nums1,nums2, 0, 1)
        );
        return ans % mod;
    }
};
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