lowest common ancestor III

class Solution:
    def divide_conquer(self, root, A, B):
        if root is None:
            return None, None
            
        left_lca_a, left_lca_b = self.divide_conquer(root.left, A, B)
        right_lca_a, right_lca_b = self.divide_conquer(root.right, A, B)
        lca_a, lca_b = None, None
        
        if (left_lca_a == None and left_lca_b != None and right_lca_a != None and right_lca_b == None) or (left_lca_a != None and left_lca_b == None and right_lca_a == None and right_lca_b != None):
            lca_a, lca_b = root, root
        
        elif left_lca_a == None and left_lca_b == None and right_lca_a == None and right_lca_b == None:
            if root == A:
                lca_a = root
            if root == B:
                lca_b = root
                
        elif left_lca_a == None and left_lca_b == None:
            if right_lca_a != None and right_lca_b != None:
                lca_a, lca_b = right_lca_a, right_lca_b
            elif right_lca_a != None:
                lca_a = right_lca_a
                if root == B:
                    lca_b, lca_a = root, root
            elif right_lca_b != None:
                lca_b = right_lca_b
                if root == A:
                    lca_a, lca_b = root, root
                    
        elif right_lca_a == None and right_lca_b == None:
            if left_lca_a != None and left_lca_b != None:
                lca_a, lca_b = left_lca_a, left_lca_b
            elif left_lca_a != None:
                lca_a = left_lca_a
                if root == B:
                    lca_b, lca_a = root, root
            elif left_lca_b != None:
                lca_b = left_lca_b
                if root == A:
                    lca_a, lca_b = root, root
                    
        return lca_a, lca_b
            
    """
    @param: root: The root of the binary tree.
    @param: A: A TreeNode
    @param: B: A TreeNode
    @return: Return the LCA of the two nodes.
    """
    def lowestCommonAncestor3(self, root, A, B):
        # write your code here
        lca_a, lca_b = self.divide_conquer(root, A, B)
        if lca_a == lca_b and lca_a is not None:
            return lca_a
        return None