K’th Largest Element in BST when modification to BST is not allowed

Given a Binary Search Tree (BST) and a positive integer k, find the k’th largest element in the Binary Search Tree.

      [20]
      /  \     
    [8]  [22] 
    /  \
  [5]  [10]
       /  \
     [9]  [12]

For example, in the following BST, if
if k = 3, then output should be 12
if k = 5, then output should be 9.