<p>You are given an array <code>nums</code> consisting of non-negative integers. You are also given a <code>queries</code> array, where <code>queries[i] = [x<sub>i</sub>, m<sub>i</sub>]</code>.</p>

<p>The answer to the <code>i<sup>th</sup></code> query is the maximum bitwise <code>XOR</code> value of <code>x<sub>i</sub></code> and any element of <code>nums</code> that does not exceed <code>m<sub>i</sub></code>. In other words, the answer is <code>max(nums[j] XOR x<sub>i</sub>)</code> for all <code>j</code> such that <code>nums[j] &lt;= m<sub>i</sub></code>. If all elements in <code>nums</code> are larger than <code>m<sub>i</sub></code>, then the answer is <code>-1</code>.</p>

<p>Return <em>an integer array </em><code>answer</code><em> where </em><code>answer.length == queries.length</code><em> and </em><code>answer[i]</code><em> is the answer to the </em><code>i<sup>th</sup></code><em> query.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [0,1,2,3,4], queries = [[3,1],[1,3],[5,6]]
<strong>Output:</strong> [3,3,7]
<strong>Explanation:</strong>
1) 0 and 1 are the only two integers not greater than 1. 0 XOR 3 = 3 and 1 XOR 3 = 2. The larger of the two is 3.
2) 1 XOR 2 = 3.
3) 5 XOR 2 = 7.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,2,4,6,6,3], queries = [[12,4],[8,1],[6,3]]
<strong>Output:</strong> [15,-1,5]
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length, queries.length &lt;= 10<sup>5</sup></code></li>
	<li><code>queries[i].length == 2</code></li>
	<li><code>0 &lt;= nums[j], x<sub>i</sub>, m<sub>i</sub> &lt;= 10<sup>9</sup></code></li>
</ul>

import numpy as np
class Solution:
    def maximizeXor(self, nums: List[int], queries: List[List[int]]) -> List[int]:
        def insert(x, trie):
            root = trie
            bits = [int(i) for i in bin(x)[2:].zfill(32)]
            for i in bits:
                if i not in root:
                    root[i] = {}
                root = root[i]
            root['$'] = x
        
        def query(x, trie):
            root = trie
            bits = [1-int(i) for i in bin(x)[2:].zfill(32)]
            res = 0
            if not trie:
                return -1
            for i in bits:
                if i in root:
                    root = root[i]
                else:
                    root = root[1-i]
            return x ^ root['$']
        
        nums = sorted(list(set(nums)))
        res = [0] * len(queries)
        queries =sorted( [(m,x,i) for i, (x,m) in enumerate(queries)])
        idx = 0
        trie = {}
        for m,x,i in queries:
            while idx<len(nums) and nums[idx] <= m:
                insert(nums[idx], trie)
                idx += 1
            res[i] = query(x, trie)
        return res
            
365681