<p>You are given the <code>root</code> of a <strong>binary search tree </strong>and an array <code>queries</code> of size <code>n</code> consisting of positive integers.</p>

<p>Find a <strong>2D</strong> array <code>answer</code> of size <code>n</code> where <code>answer[i] = [min<sub>i</sub>, max<sub>i</sub>]</code>:</p>

<ul>
	<li><code>min<sub>i</sub></code> is the <strong>largest</strong> value in the tree that is smaller than or equal to <code>queries[i]</code>. If a such value does not exist, add <code>-1</code> instead.</li>
	<li><code>max<sub>i</sub></code> is the <strong>smallest</strong> value in the tree that is greater than or equal to <code>queries[i]</code>. If a such value does not exist, add <code>-1</code> instead.</li>
</ul>

<p>Return <em>the array</em> <code>answer</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/09/28/bstreeedrawioo.png" style="width: 261px; height: 281px;" />
<pre>
<strong>Input:</strong> root = [6,2,13,1,4,9,15,null,null,null,null,null,null,14], queries = [2,5,16]
<strong>Output:</strong> [[2,2],[4,6],[15,-1]]
<strong>Explanation:</strong> We answer the queries in the following way:
- The largest number that is smaller or equal than 2 in the tree is 2, and the smallest number that is greater or equal than 2 is still 2. So the answer for the first query is [2,2].
- The largest number that is smaller or equal than 5 in the tree is 4, and the smallest number that is greater or equal than 5 is 6. So the answer for the second query is [4,6].
- The largest number that is smaller or equal than 16 in the tree is 15, and the smallest number that is greater or equal than 16 does not exist. So the answer for the third query is [15,-1].
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/09/28/bstttreee.png" style="width: 101px; height: 121px;" />
<pre>
<strong>Input:</strong> root = [4,null,9], queries = [3]
<strong>Output:</strong> [[-1,4]]
<strong>Explanation:</strong> The largest number that is smaller or equal to 3 in the tree does not exist, and the smallest number that is greater or equal to 3 is 4. So the answer for the query is [-1,4].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[2, 10<sup>5</sup>]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 10<sup>6</sup></code></li>
	<li><code>n == queries.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= queries[i] &lt;= 10<sup>6</sup></code></li>
</ul>

from typing import Optional, List

# Definition for a binary tree node.
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

class Solution:
    def closestNodes(self, root: Optional[TreeNode], queries: List[int]) -> List[List[int]]:
        # Helper function to perform inorder traversal
        def inorder(node: Optional[TreeNode], sorted_values: List[int]):
            if not node:
                return
            inorder(node.left, sorted_values)
            sorted_values.append(node.val)
            inorder(node.right, sorted_values)
        
        # Perform inorder traversal to get sorted values
        sorted_values = []
        inorder(root, sorted_values)
        
        # Function to find the largest value <= target
        def find_max_leq(target: int) -> int:
            low, high = 0, len(sorted_values) - 1
            result = -1
            while low <= high:
                mid = (low + high) // 2
                if sorted_values[mid] <= target:
                    result = sorted_values[mid]
                    low = mid + 1
                else:
                    high = mid - 1
            return result
        
        # Function to find the smallest value >= target
        def find_min_geq(target: int) -> int:
            low, high = 0, len(sorted_values) - 1
            result = -1
            while low <= high:
                mid = (low + high) // 2
                if sorted_values[mid] >= target:
                    result = sorted_values[mid]
                    high = mid - 1
                else:
                    low = mid + 1
            return result
        
        # Process each query
        answer = []
        for query in queries:
            mini = find_max_leq(query)
            maxi = find_min_geq(query)
            answer.append([mini, maxi])
        
        return answer
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