You are given the `root`

node of a binary search tree (BST) and a `value`

to insert into the tree. Return *the root node of the BST after the insertion*. It is **guaranteed** that the new value does not exist in the original BST.

**Notice** that there may exist multiple valid ways for the insertion, as long as the tree remains a BST after insertion. You can return **any of them**.

**Example 1:**

Input:root = [4,2,7,1,3], val = 5Output:[4,2,7,1,3,5]Explanation:Another accepted tree is:

**Example 2:**

Input:root = [40,20,60,10,30,50,70], val = 25Output:[40,20,60,10,30,50,70,null,null,25]

**Example 3:**

Input:root = [4,2,7,1,3,null,null,null,null,null,null], val = 5Output:[4,2,7,1,3,5]

**Constraints:**

- The number of nodes in the tree will be in the range
`[0, 10`

.^{4}] `-10`

^{8}<= Node.val <= 10^{8}- All the values
`Node.val`

are**unique**. `-10`

^{8}<= val <= 10^{8}- It's
**guaranteed**that`val`

does not exist in the original BST.