<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 {
public:
    vector<int> maximizeXor(vector<int>& nums, vector<vector<int>>& queries) {
        //sort by bits
        //binary search by bits and depth
        std::ranges::sort(nums);
        std::vector<int> ans;
        ans.reserve(queries.size());
        for(std::vector<int>& query : queries){
            if(query.back()<nums.front()){
                ans.push_back(-1);
                continue;
            }
            int num = query.front();
            int low = 0;
            int high = std::lower_bound(nums.begin(),nums.end(),query.back())-nums.begin();
            if(high > nums.size() || nums[high]!=query.back())high--;
            int bit = 0;
            while(query.back()){
                bit++;
                query.back()>>=1;
            }
            for(int i = bit-1;i>=0 && low != high;i--){
                bool flag = num&(1<<i);
                if(flag && (!((*(nums.begin()+low))&(1<<i)) || !((*(nums.begin()+high))&(1<<i)))){
                    high = std::prev(std::lower_bound(nums.begin()+low,nums.begin()+high+1,(1<<i),[](int num,int bit){
                        return !(num&bit);
                    }))-nums.begin();
                }else if(((*(nums.begin()+low))&(1<<i)) || ((*(nums.begin()+high))&(1<<i))){
                    low = std::lower_bound(nums.begin()+low,nums.begin()+high+1,(1<<i),[](int num,int bit){
                        return !(num&bit);
                    })-nums.begin();
                }
            }
            ans.push_back(num^nums[low]);
        }
        return ans;
    }
};
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