<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>


from typing import Callable

set_bit_at: Callable[[int, int], int] = lambda n, at: n | (1 << at)
get_bit_at: Callable[[int, int], bool] = lambda n, at: n & (1 << at) != 0


class Node:
    child0: "Node | None" = None
    child1: "Node | None" = None
    min0: int = 2 << 30
    min1: int = 2 << 30

    # def __init__(self):
    def put(self, bit: bool, node: "Node") -> None:
        if bit:
            self.child1 = node
        else:
            self.child0 = node


class Trie:
    def __init__(self):
        self.root: Node = Node()

    def insert(self, n: int) -> None:
        cn: Node = self.root  # current node
        for i in range(30, -1, -1):
            bit: bool = False
            if get_bit_at(n, i):
                bit = True
                cn.min1 = min(cn.min1, n)
            else:
                cn.min0 = min(cn.min0, n)

            if bit:
                if not cn.child1:
                    cn.child1 = Node()
                cn = cn.child1
            else:
                if not cn.child0:
                    cn.child0 = Node()
                cn = cn.child0

    def find_max(self, a: int, mx: int) -> int:
        cn: Node = self.root  # current node
        ans: int = 0
        for i in range(30, -1, -1):
            mini0: int = cn.min0
            mini1: int = cn.min1

            if get_bit_at(a, i) and cn.child0 and mini0 <= mx:
                cn = cn.child0
                ans = set_bit_at(ans, i)
            elif not get_bit_at(a, i) and cn.child1 and mini1 <= mx:
                cn = cn.child1
                ans = set_bit_at(ans, i)
            elif not get_bit_at(a, i) and cn.child0 and mini0 <= mx:
                cn = cn.child0
            elif get_bit_at(a, i) and cn.child1 and mini1 <= mx:
                cn = cn.child1

            else:
                return -1
        return ans


class Solution:
    def maximizeXor(self, nums: list[int], queries: list[list[int]]) -> list[int]:
        t = Trie()
        for num in nums:
            t.insert(num)
        return [t.find_max(*q) for q in queries]


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