<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
ll mod=1e9+7;
ll dp[100001][2];
ll n,m;
unordered_map<int,int> mp,mp1,mp2;
ll f(int i,int fl,vector<int> &v1,vector<int> &v2){
    if((i==n and fl==0 ) or (i==m and fl==1)){
        return 0;
    }
    if(dp[i][fl]!=-1){
        return dp[i][fl];
    }
    ll way1;
    if(fl==0){
        way1=(v1[i]+f(i+1,fl,v1,v2));
    }
    else{
        way1=(v2[i]+f(i+1,fl,v1,v2));
    }
    ll way2=0;
    if(fl==0 and mp[v1[i]]>1){
        way2=(v1[i]+f(mp2[v1[i]]+1,1,v1,v2));
    }
    else if(fl==1 and mp[v2[i]]>1){
        way2=(v2[i]+f(mp1[v2[i]]+1,0,v1,v2));
    }
    return dp[i][fl]=(max(way1,way2));
}
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
       n=nums1.size(),m=nums2.size(); 
       memset(dp,-1,sizeof(dp));
       for(int i=0;i<n;i++){
        mp[nums1[i]]++;
        mp1[nums1[i]]=i;
       }
       for(int i=0;i<m;i++){
        mp[nums2[i]]++;
        mp2[nums2[i]]=i;
       }
       ll k1=f(0,0,nums1,nums2)%mod;
       ll k2=f(0,1,nums1,nums2)%mod;
       return max(k1,k2);
    }
};
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