<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>

class Solution {
public:
    static const int MOD = 1e9 + 7; // Define the modulo constant

    // Store the subtree sums
    unordered_map<TreeNode*, int> subtreeSumMap;
    
    // Helper function to calculate the sum of all nodes in the tree
    int calculateSum(TreeNode* root) {
        if (root == nullptr) {
            return 0;
        }
        // Calculate subtree sum for the current node
        int leftSum = calculateSum(root->left);
        int rightSum = calculateSum(root->right);
        int totalSum = root->val + leftSum + rightSum;
        subtreeSumMap[root] = totalSum; // Store the sum for this subtree
        return totalSum;
    }
    
    void findGreatest(TreeNode* root, long long& grt, int totalSum) {
        if (root == nullptr) {
            return;
        }
        
        // Get the precomputed sums
        int leftSum = (root->left) ? subtreeSumMap[root->left] : 0;
        int rightSum = (root->right) ? subtreeSumMap[root->right] : 0;
        
        // Calculate potential products
        long long leftProduct = (long long)leftSum * (totalSum - leftSum);
        long long rightProduct = (long long)rightSum * (totalSum - rightSum);
        
        // Update the maximum product found
        grt = max(grt, max(leftProduct, rightProduct));
        
        // Recur for left and right subtrees
        findGreatest(root->left, grt, totalSum);
        findGreatest(root->right, grt, totalSum);
    }

    int maxProduct(TreeNode* root) {
        int totalSum = calculateSum(root);
        long long maxProduct = 0;
        findGreatest(root, maxProduct, totalSum);
        return maxProduct % MOD; // Apply modulo operation to the final result
    }
};

102473