<p>Given the <code>root</code> of a binary tree, split the binary tree into two subtrees by removing one edge such that the product of the sums of the subtrees is maximized.</p>

<p>Return <em>the maximum product of the sums of the two subtrees</em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p><strong>Note</strong> that you need to maximize the answer before taking the mod and not after taking it.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/01/21/sample_1_1699.png" style="width: 500px; height: 167px;" />
<pre>
<strong>Input:</strong> root = [1,2,3,4,5,6]
<strong>Output:</strong> 110
<strong>Explanation:</strong> Remove the red edge and get 2 binary trees with sum 11 and 10. Their product is 110 (11*10)
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/01/21/sample_2_1699.png" style="width: 500px; height: 211px;" />
<pre>
<strong>Input:</strong> root = [1,null,2,3,4,null,null,5,6]
<strong>Output:</strong> 90
<strong>Explanation:</strong> Remove the red edge and get 2 binary trees with sum 15 and 6.Their product is 90 (15*6)
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[2, 5 * 10<sup>4</sup>]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 10<sup>4</sup></code></li>
</ul>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */

class Solution {
public:
    
   long long int ans;
    long long int modulo = 1000000007;

    long long int solve(TreeNode* root,long long int total,long long int&ans)
    {
        if(root==NULL)
        {
            return 0;
        }
         
        
       long long int left = solve(root->left,total,ans);
      long long  int right = solve(root->right,total,ans);

        
        ans = max(ans,(left*(total-left)));
       
      
         ans = max(ans,(right*(total-right)));
        
        int sum = root->val+left+right;

        ans = max(ans,(sum*(total-sum)));
        return root->val+left+right;
  

       
    }
    int maxProduct(TreeNode* root) {

        if(root==NULL)
        {
            return 0;
        }
        
        ans = -1;
        queue<TreeNode*> q;
        q.push(root);
        int total = 0;
        while(!q.empty())
        {
            int size = q.size();
            for(int i=0;i<size;i++)
            {
                TreeNode* curr = q.front();
                q.pop();
                total+=curr->val;

                if(curr->left)
                {
                    q.push(curr->left);
                }

                if(curr->right)
                {
                    q.push(curr->right);
                }
            }

        }
        
        
        solve(root,total,ans);

       
        
        return ans%modulo;
    }
};
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