<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:

    long long solve(vector<int>&nums1, vector<int>&nums2, long long i, bool one, vector<long long>&dp1, vector<long long>&dp2){
        if((one && i >= nums1.size()) || (!one && i >= nums2.size())){
            return 0;
        }   
        //
        // if(dp[i][one] != -1) return dp[i][one];
        if(one && dp1[i] != -1){
            return dp1[i];
        }
        else if(!one && dp2[i] != -1){
            return dp2[i];
        }
        long long M = 1e9 + 7;
        if(one){
            long long t1 = (((long long)nums1[i]) + solve(nums1, nums2, i+1, one, dp1, dp2));
            long long t2 = 0;
            long long ind = lower_bound(nums2.begin(), nums2.end(), nums1[i]) - nums2.begin();
            if(ind == nums2.size() || nums2[ind] != nums1[i]){

            }
            else{
                t2 = (((long long)nums1[i]) + solve(nums1, nums2, ind+1, !one, dp1, dp2));
            }
            return dp1[i] = max(t1, t2);
        }
        else{
            long long t1 = (((long long)nums2[i]) + solve(nums1, nums2, i+1, one, dp1, dp2));
            long long t2 = 0;
            long long ind = lower_bound(nums1.begin(), nums1.end(), nums2[i]) - nums1.begin();
            if(ind == nums1.size() || nums1[ind] != nums2[i]){

            }
            else{
                t2 = (((long long)nums2[i]) + solve(nums1, nums2, ind+1, !one, dp1, dp2));
            }
            return dp2[i] = max(t1, t2);
        }
        return 0;
    }

    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        vector<long long> dp1(nums1.size(), -1);
        vector<long long> dp2(nums2.size(), -1);
        long long M = 1e9 + 7;
        return max(solve(nums1, nums2, 0, 1, dp1, dp2), solve(nums1, nums2, 0, 0, dp1, dp2))%M;
    }
};
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