Delete Edge!

Given an undirected tree with N nodes labeled from 1 to N.

Each node has a certain weight assigned to it given by an integer array A of size N.

You need to delete an edge in such a way that the Product between the sum of weights of nodes in one subtree with the sum of weights of nodes in other subtree is maximized.

Return this maximum possible product modulo 10⁹ + 7.

NOTE:

• The tree is rooted at a node labeled with 1.
• You need to return the maximum possible product, then take its mod.

2 <= N <= 10⁵

1 <= A[i] <= 10³

First argument is an integer array A of size N denoting the weight of each node.

Second argument is a 2-D array B of size (N-1) x 2 denoting the edge of the tree.

Return a single integer denoting the maximum product prossible of sum of weights of nodes in the two subtrees formed by deleting an edge with modulo 10⁹ + 7.

Input 1:

 A = [10, 5, 12, 6]
 B = [

        [1, 2]
        [1, 4]
        [4, 3]
     ]

Input 2:

 A = [11, 12]
 B = [

        [1, 2]
     ]

Output 1:

 270

Output 2:

 132

Explanation 1:

 Removing edge (1, 4) created two subtrees.
 Subtree-1 contains nodes (1, 2) and Subtree-2 contains nodes (3, 4)
 So product will be = (A[1] + A[2]) * (A[3] + A[4]) = 15 * 18 = 270

Explanation 2:

 Removing edge (1, 2) created two subtrees.
 Subtree-1 contains node (1) and Subtree-2 contains node (3)
 So product will be = (A[1]) * (A[2]) = 11 * 12 = 132