<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>

class Solution:
    def maximizeXor(self, nums: List[int], queries: List[List[int]]) -> List[int]:
        
        maxx = 0
        for i, q in enumerate(queries):
            maxx = max(maxx, q[0])
            queries[i].append(i)
        
        queries.sort(key = lambda x: x[1])

        Trie = lambda: collections.defaultdict(Trie)
        trie = Trie()
        
        nums.sort()
        L = max(nums[-1].bit_length(), maxx.bit_length())
        i = 0
        
        def get_bin(n, L):
            bins = []

            while n:
                bins.append(n % 2)
                n //= 2

            while len(bins) < L:
                bins.append(0)

            return bins[::-1]
        
        res = [-1] * (len(queries))
        
        
        for q in queries:
            x, m, idx = q

            while i < len(nums) and nums[i] <= m:
                bins = get_bin(nums[i], L)
                curr = trie
                for k in bins:
                    curr = curr[k]
                i += 1
                
            # do the searching
            bins = get_bin(x, L)
            curr = trie
            path = []
            
            if i == 0:
                res[idx] = -1
            else:
                for k in bins:
                    if 1 - k in curr:
                        curr = curr[1-k]
                        path.append("1")
                    else:
                        curr = curr[k]
                        path.append("0")

                res[idx] = int("".join(path),2)
                
        return res
                        
        
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