<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>

static const int mod = 1e9+7;
class Solution {
public:
    vector<vector< long long>> dp; 
    long long g(vector<int>& nList1,vector<int>& nList2,vector<int>& idxList1,vector<int>& idxList2,
                int on1,int idx){
        long long ret = 0;
        if(on1){
            if(idx >= nList1.size()){
                return 0;
            }
            else{
                if(dp[on1][idx] != -1){
                    return dp[on1][idx];
                }
                ret = g(nList1,nList2,idxList1,idxList2,on1,idx+1) + nList1[idx];
                int cur = nList1[idx];
                if(idxList1[idx] != -1){
                    ret = max(ret , g(nList1,nList2,idxList1,idxList2,0,idxList1[idx]+1) + cur);
                }

            }
        }
        else{
            if(idx >= nList2.size()){
                return 0;
            }
            else{
                if(dp[on1][idx] != -1){
                    return dp[on1][idx];
                }
                int cur = nList2[idx];
                ret = g(nList1,nList2,idxList1,idxList2,on1,idx+1) + cur;
                if(idxList2[idx] != -1){
                    ret = max(ret, g(nList1,nList2,idxList1,idxList2,1,idxList2[idx] + 1) + cur);
                }
            }
        }
        dp[on1][idx] = ret;;
        return ret;
    }
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        map<int,int> idxMap1;
        map<int,int> idxMap2;
        vector<int> idxList1(nums1.size(),-1);
        vector<int> idxList2(nums2.size(),-1);
        
        for(int i = 0;i < nums1.size(); ++i){
            idxMap1[nums1[i]] = i;
        }
        for(int i = 0;i < nums2.size();++i){
            if(idxMap1.count(nums2[i])){
                int idx1 = idxMap1[nums2[i]];
                idxList1[idx1] = i;
                idxList2[i] = idx1;
            }
        }
        auto len = max(nums1.size() , nums2.size());
        dp.resize(2,vector<long long>(len,-1));
        auto op1 = g(nums1,nums2,idxList1,idxList2,0,0);
        auto op2 = g(nums1,nums2,idxList1,idxList2,1,0);
        auto ret = max(op1,op2);
        return ret % mod;
    }
};
96666