Cut BST

Given a Binary Search Tree, and an integer k, cut the BST vertically into two substrees A and B, where all nodes in A <= k and all nodes in B > k.

Contrain: for any node A and it’s parent B in the original BST. If after the cut they are both in the same subtree. B should still be the parent of A.

example:

Input:

           50

        /         \

      20          60

     /   \         /  \

   10   30   55   70

k = 50

output:

      20         

     /   \        

   10   30   

and 

      60

     /   \         

   55   70