<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:
    unordered_map<int, int> path1;
    unordered_map<int, int> path2;
    int n, m;
    int mod = 1e9+7;
    
    long long int solve(vector<int>& nums1, vector<int>& nums2, int index, int path, vector<vector<long long int>>& dp) {
        if(path == 1) {
            if(index >= n) return 0;
        }
        if(path == 2) {
            if(index >= m) return 0;
        }
        if(dp[index][path] != -1) return dp[index][path];
        if(path == 1) {
            long long stay = nums1[index] + solve(nums1, nums2, index+1, 1, dp);
            long long change = 0;
            if(path2.find(nums1[index]) != path2.end()) {
                change = nums1[index] + solve(nums1, nums2, path2[nums1[index]]+1, 2, dp);
            }
            return dp[index][path] = max(stay, change);
        }
        else {
            long long stay = nums2[index] + solve(nums1, nums2, index+1, 2, dp);
            long long change = 0;
            if(path1.find(nums2[index]) != path1.end()) {
                change = nums2[index] + solve(nums1, nums2, path1[nums2[index]]+1, 1, dp);
            }
            return dp[index][path] = max(stay, change);
        }
    }
    
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        n = nums1.size();
        m = nums2.size();
        int maxLen = max(n, m);
        vector<vector<long long int>> dp(maxLen+1, vector<long long int>(3, -1));
        for(int i=0;i<n;++i) {
            path1[nums1[i]] = i;
        }
        for(int i=0;i<m;++i) {
            path2[nums2[i]] = i;
        }
        long long int res1 = solve(nums1, nums2, 0, 1, dp) % mod;
        long long int res2 = solve(nums1, nums2, 0, 2, dp) % mod;
        return max(res1, res2) % mod;
    }
};
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