<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:
    def maxSum(self, nums1: List[int], nums2: List[int]) -> int:
        # greey, always pick the largest path sum to the point where nums1 and nums2 intersect
        # each other: the two array have the same number
        n1_len, n2_len = len(nums1), len(nums2)
        n1_set, n2_set = set(nums1), set(nums2)
        n12_intersect = n1_set.intersection(n2_set)
        n12_intersect_loc = collections.defaultdict(list)
        
        n1_prefix_sum = [0]
        n2_prefix_sum = [0]
        
        idx, rs = 0, 0
        while idx < n1_len:
            rs += nums1[idx]
            n1_prefix_sum.append(rs)
            if nums1[idx] in n12_intersect:
                n12_intersect_loc[nums1[idx]].append(idx + 1)
            idx += 1
        
        idx, rs = 0, 0
        while idx < n2_len:
            rs += nums2[idx]
            n2_prefix_sum.append(rs)
            if nums2[idx] in n12_intersect:
                n12_intersect_loc[nums2[idx]].append(idx + 1)
            idx += 1
        
        # if there is no intersection between nums1 and nums2
        if len(n12_intersect_loc) == 0:
            return max(n1_prefix_sum[-1], n2_prefix_sum[-1])
        
        ans = 0
        # there are intersections between nums1 and nums2
        n1_prev_idx, n2_prev_idx = 0, 0
        for i_num in n12_intersect_loc:
            n1_loc, n2_loc = n12_intersect_loc[i_num]
            ans += max((n1_prefix_sum[n1_loc] - n1_prefix_sum[n1_prev_idx]), (n2_prefix_sum[n2_loc] - n2_prefix_sum[n2_prev_idx]))
            n1_prev_idx = n1_loc
            n2_prev_idx = n2_loc
        
        ans += max((n1_prefix_sum[-1] - n1_prefix_sum[n1_prev_idx]), (n2_prefix_sum[-1] - n2_prefix_sum[n2_prev_idx]))
        
        return ans % (1000000007)
37800