<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 {

unordered_map<int, int> idx[2];
long long dp[2][100005];
int n[2];
vector<int> a[2];

const int mod = 1e9 + 7;

long long solve(int ty, int i) {
	if (dp[ty][i] > -1) {
		return dp[ty][i];
	}
	if (i >= n[ty]) {
		return 0;
	}
	int x = a[ty][i];
	long long res = x + solve(ty, i + 1);
	auto it = idx[ty ^ 1].find(x);
	if (it != idx[ty ^ 1].end()) {
		res = max(res, x + solve(ty ^ 1, it->second + 1));
	}
	return dp[ty][i] = res;
}

public:
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
  		n[0] = nums1.size(), n[1] = nums2.size();
  		a[0] = nums1, a[1] = nums2;

  		for (int i = 0; i < n[0]; i++) {
  			idx[0][nums1[i]] = i;
  			dp[0][i] = -1;
  		}	      
  		for (int i = 0; i < n[1]; i++) {
  			idx[1][nums2[i]] = i;
  			dp[1][i] = -1;
  		}
  		long long ans = max(solve(0, 0), solve(1, 0));
  		return ans % mod;
    }
};



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