I think that I can add 38 and 40 as a child of 39 and I can add 113 as a child of 112, Am I correct? Or there are other possible solutions to this question? Please explain it clearly and in detail. You can use a paper explanation for this question. TY.

Question: Given a BST, there are some keys that, if inserted, will increase the height of the tree. For the BST below, list all the integer keys (distinct from those already in the tree) for which this is true. If no such keys exists, explain why not. (Each key should increase the height if inserted alone, not with other keys.) 95 / 1 40 113 / / . 37 42 111 125 39 112