<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 {
    int mod =  1e9 + 7;
    int firstMatch(vector<int>& nums1, vector<int>& nums2)
    {
        int i = 0;
        int j = 0;

        while(i < nums1.size() && j < nums2.size())
        {
            if(nums1[i] == nums2[j])
            {
                return nums1[i];
            }
            else if(nums1[i] < nums2[j])
            {
                i++;
            }
            else
            {
                j++;
            }
        }
        return -1;
    }

    void Common(vector<int>& nums1, vector<int>& nums2, unordered_set<int>& st)
    {
        int i = 0;
        int j = 0;
        while(i < nums1.size() && j < nums2.size())
        {
            if(nums1[i] == nums2[j])
            {
                st.insert(nums1[i]);
                i++;
                j++;
            }

            else if(nums1[i] < nums2[j])
            {
                i++;
            }
            else
            {
                j++;
            }
        }
    }
public:
    int maxSum(vector<int>& nums1, vector<int>& nums2) {
        int n = nums1.size();
        int m = nums2.size();
        unordered_set<int> st;
        Common(nums1, nums2, st);

        vector<long long int> preSum1(n);
        preSum1[n-1] = nums1[n-1];

        for(int i=n-2;i>=0;i--)
        {
            preSum1[i] = preSum1[i+1] + nums1[i];
        }

        vector<long long int> preSum2(m);
        preSum2[m-1] = nums2[m-1];

        for(int i=m-2;i>=0;i--)
        {
            preSum2[i] = preSum2[i+1] + nums2[i];
        }

        int Match = firstMatch(nums1,nums2);

        if(Match == -1)
        {
            if(preSum1[0] > preSum2[0])
            {
                return preSum1[0]%mod;
            }
            return preSum2[0]%mod;
        }

        int i = 0, j = 0;
        long long sum1 = 0, sum2 = 0, maxSum = 0;
        bool flag = true; 

        while (i < n || j < m) {
            if (i < n && j < m && nums1[i] == nums2[j]) {
                maxSum += max(sum1, sum2) + nums1[i];
                maxSum %= mod;
                sum1 = sum2 = 0;  
                i++;
                j++;
            } else if (i < n && (j >= m || nums1[i] < nums2[j])) {
                sum1 += nums1[i++];
            } else {
                sum2 += nums2[j++];
            }
        }

        maxSum += max(sum1, sum2);
        return maxSum % mod;
    }
};
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