<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:
const int mod=1e9+7;
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        unordered_map<int,int> mp,ind1,ind2;
        for(int i=0;i<nums1.size();i+=1){
            ind1[nums1[i]]=i;
        }
        for(int i=0;i<nums2.size();i+=1){
            ind2[nums2[i]]=i;
        }
        for(auto i:nums1)mp[i]+=1;
        for(auto i:nums2)mp[i]+=1;
        vector<int> first(nums1.size(),-1);
        vector<int> second(nums2.size(),-1);
        vector<long long int> pref_first(nums1.size(),0),pref_second(nums2.size(),0);
        long long int sum=0;
        for(int i=0;i<nums1.size();i+=1){
            sum+=nums1[i];
            pref_first[i]=sum;
        }
        sum=0;
        for(int i=0;i<nums2.size();i+=1){
            sum+=nums2[i];
            pref_second[i]=sum;
        }
        int curr=-1;
        for(int i=nums1.size()-1;i>=0;i-=1){
            first[i]=curr;
            if(mp[nums1[i]]==2)curr=i;
        }
        curr=-1;
        for(int i=nums2.size()-1;i>=0;i-=1){
            second[i]=curr;
            if(mp[nums2[i]]==2)curr=i;
        }
        curr=0;
        sum=0;
        long long int ans=0;
        int i=0;
        int j=0;
        while(i<nums1.size() and j<nums2.size()){
            cout<<i<<" "<<j<<" "<<curr<<endl;
            if(curr==0){
                if(mp[nums1[i]]==1){
                    sum+=nums1[i];
                    i+=1;
                }else{
                    int nf=first[i];
                    int ns=second[ind2[nums1[i]]];
                    long long int s1=0,s2=0;
                    if(nf==-1){
                        s1=pref_first[nums1.size()-1];
                        if(i-1>=0)s1-=pref_first[i-1];
                    }else{
                        s1=pref_first[nf];
                        if(i-1>=0)s1-=pref_first[i-1];
                    }
                     if(ns==-1){
                        s2=pref_second[nums2.size()-1];
                        if(ind2[nums1[i]]-1>=0)s2-=pref_second[ind2[nums1[i]]-1];
                    }else{
                        s2=pref_second[ns];
                        if(ind2[nums1[i]]-1>=0)s2-=pref_second[ind2[nums1[i]]-1];
                    }
           // cout<<s1<<" "<<s2<<" "<<nf<<" "<<ind2[nums1[i]]<<endl;
                    if(s1>=s2){
                        sum+=nums1[i];
                        i+=1;
                    }else{
                        sum+=nums2[ind2[nums1[i]]];
                        j=ind2[nums1[i]]+1;
                        curr=1;
                    }
            
                }
            }else{
                if(mp[nums2[j]]==1){
                    sum+=nums2[j];
                    j+=1;
                }else{
                    int nf=first[ind1[nums2[j]]];
                    int ns=second[j];
                    long long int s1=0,s2=0;
                    if(nf==-1){
                        s1=pref_first[nums1.size()-1];
    if(ind1[nums2[j]]-1>=0)s1-=pref_first[ind1[nums2[j]]-1];
                    }else{
                        s1=pref_first[nf];
                        if(ind1[nums2[j]]-1>=0)s1-=pref_first[ind1[nums2[j]]-1];
                    }
                     if(ns==-1){
                        s2=pref_second[nums2.size()-1];
                        if(j-1>=0)s2-=pref_second[j-1];
                    }else{
                        s2=pref_second[ns];
                        if(j-1>=0)s2-=pref_second[j-1];
                    }
                    if(s1>=s2){
                        sum+=nums1[ind1[nums2[j]]];
                        i=ind1[nums2[j]]+1;
                        curr=0;
                    }else{
                        sum+=nums2[j];
                        j+=1;
                        curr=1;
                    }
            
                }

            }
            ans=max(ans,sum);
        }   
        sum=0;
        i=0,j=0;
        curr=1;
                while(i<nums1.size() and j<nums2.size()){
           // cout<<i<<" "<<j<<" "<<curr<<endl;
            if(curr==0){
                if(mp[nums1[i]]==1){
                    sum+=nums1[i];
                    i+=1;
                }else{
                    int nf=first[i];
                    int ns=second[ind2[nums1[i]]];
                    long long int s1=0,s2=0;
                    if(nf==-1){
                        s1=pref_first[nums1.size()-1];
                        if(i-1>=0)s1-=pref_first[i-1];
                    }else{
                        s1=pref_first[nf];
                        if(i-1>=0)s1-=pref_first[i-1];
                    }
                     if(ns==-1){
                        s2=pref_second[nums2.size()-1];
                        if(ind2[nums1[i]]-1>=0)s2-=pref_second[ind2[nums1[i]]-1];
                    }else{
                        s2=pref_second[ns];
                        if(ind2[nums1[i]]-1>=0)s2-=pref_second[ind2[nums1[i]]-1];
                    }
           // cout<<s1<<" "<<s2<<" "<<nf<<" "<<ind2[nums1[i]]<<endl;
                    if(s1>=s2){
                        sum+=nums1[i];
                        i+=1;
                    }else{
                        sum+=nums2[ind2[nums1[i]]];
                        j=ind2[nums1[i]]+1;
                        curr=1;
                    }
            
                }
            }else{
                if(mp[nums2[j]]==1){
                    sum+=nums2[j];
                    j+=1;
                }else{
                    int nf=first[ind1[nums2[j]]];
                    int ns=second[j];
                    long long int s1=0,s2=0;
                    if(nf==-1){
                        s1=pref_first[nums1.size()-1];
    if(ind1[nums2[j]]-1>=0)s1-=pref_first[ind1[nums2[j]]-1];
                    }else{
                        s1=pref_first[nf];
                        if(ind1[nums2[j]]-1>=0)s1-=pref_first[ind1[nums2[j]]-1];
                    }
                     if(ns==-1){
                        s2=pref_second[nums2.size()-1];
                        if(j-1>=0)s2-=pref_second[j-1];
                    }else{
                        s2=pref_second[ns];
                        if(j-1>=0)s2-=pref_second[j-1];
                    }
                    if(s1>=s2){
                        sum+=nums1[ind1[nums2[j]]];
                        i=ind1[nums2[j]]+1;
                        curr=0;
                    }else{
                        sum+=nums2[j];
                        j+=1;
                        curr=1;
                    }
            
                }

            }
            ans=max(ans,sum);
        }   
        return (ans)%mod;
    }
};
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