<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:
    #define ll long long
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        unordered_map <int, int> map,map2;
        int n = nums1.size();
       // long long ans = 0;
        vector<vector<long long>> dp(max(nums1.size(),nums2.size()), vector<ll>(2,0));
        int i = n-1,j = nums2.size()-1;
        while(i>=0 || j>=0){
         //   cout<<i<<" "<<j<<endl;
            if(j>=0 && (i<0 || nums2[j]>nums1[i])){
                ll ans = nums2[j];
                if(j+1<nums2.size()){
                    ans += dp[j+1][1];
                }
            dp[j][1] = ans;
            j--;
            }
            else if(i>=0 && (j<0 || nums1[i]>nums2[j])){
                ll ans = nums1[i];
                if(i+1<n){
                    ans+=dp[i+1][0];
                }
               // cout<<"test :"<<ans<<endl;
                dp[i][0] = ans;
                i--;
            }
            else{
                ll ans = 0;
                if(i+1<n){
                    ans = max(ans,dp[i+1][0]);
                }
                if(j+1<nums2.size()){
                    ans = max(ans,dp[j+1][1]);
                }
            //    cout<<"test :"<<ans<<" "<<nums1[j]<<endl;
                ans+=nums1[i];
                dp[i][0] = ans;dp[j][1] = ans;
                i--;j--;
            }
        }
        int MOD = 1e9 + 7;
        dp[0][0]%=MOD;
        dp[0][1]%=MOD;

        return (int)max(dp[0][0],dp[0][1]);
    }
};
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