Given the root of a binary search tree and a floating point target value, find the node value in the BST that is closest to target. If there are multiple node values with the same minimum distance to target, return the smallest among them.

Note: The target is a floating point number, while all node values are integers.

Constraints:

• The number of nodes in the tree is in the range $[1, 10^4]$.

• $0 \leq$ Node.val $\leq 10^9$

• $-10^9 \leq$ target $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.