package q1339

type TreeNode struct {
	Val   int
	Left  *TreeNode
	Right *TreeNode
}

func sumSumTrees(node *TreeNode) int {
	if node == nil {
		return 0
	}
	node.Val += sumSumTrees(node.Left) + sumSumTrees(node.Right)
	return node.Val
}

func findNearest(node *TreeNode, target int) int {
	if node == nil {
		return -1
	}
	ret := node.Val
	l, r := findNearest(node.Left, target), findNearest(node.Right, target)
	if abs(l-target) < abs(ret-target) {
		ret = l
	}
	if abs(r-target) < abs(ret-target) {
		ret = r
	}
	return ret
}

func abs(n int) int {
	if n < 0 {
		return -n
	}
	return n
}

func maxProduct(root *TreeNode) int {
	totalSum := sumSumTrees(root)
	nearest := findNearest(root, totalSum/2)
	return nearest * (totalSum - nearest) % (1e9 + 7)
}

var _ = maxProduct