<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>

class Solution:
    def closestNodes(self, root, queries):
        # Helper function to perform in-order traversal of the BST
        def dfs(node, arr):
            if not node:
                return
            dfs(node.left, arr)  # Traverse left subtree
            arr.append(node.val)  # Visit node
            dfs(node.right, arr)  # Traverse right subtree

        # Step 1: Traverse the BST and store the values in a sorted array
        sorted_values = []
        dfs(root, sorted_values)

        # Step 2: Initialize the answer list
        answer = []
        n = len(sorted_values)

        # Step 3: Process each query
        for query in queries:
            left, right = 0, n - 1
            # Step 4: Perform binary search to find the closest nodes
            while left <= right:
                mid = (left + right) // 2
                if sorted_values[mid] == query:
                    break
                elif sorted_values[mid] > query:
                    right = mid - 1
                else:
                    left = mid + 1

            # Step 5: Determine the closest nodes based on the binary search result
            if sorted_values[mid] == query:
                answer.append([sorted_values[mid], sorted_values[mid]])
            elif sorted_values[mid] > query:
                if mid - 1 >= 0:
                    answer.append([sorted_values[mid - 1], sorted_values[mid]])
                else:
                    answer.append([-1, sorted_values[mid]])
            else:
                if mid + 1 < n:
                    answer.append([sorted_values[mid], sorted_values[mid + 1]])
                else:
                    answer.append([sorted_values[mid], -1])

        return answer
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