<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 node {
    public:
    node *links[2];
    node() {
        links[0]=NULL;
        links[1]=NULL;
    }
};

class trie {
    public:
    node *root;
    trie() {
        root = new node();
    }
    void insert(int &n) {
        node *temp = root;
        for(int i = 31;i>=0;i--) {
            int bit = 0;
            if((1<<i)&n) bit = 1;
            if(!temp->links[bit]) temp->links[bit] = new node();
            temp = temp->links[bit];            
        }        
    }
    int check(node *curr,int i, int &x, int &m,int ans, int other) {
        if(i<0  && other<=m) return ans;
        if(i<0) return -1;        
        if(!curr) return -1;
        if(other>m) return -1;

        int bit = 0;
        if((1<<i)&x) bit = 1;
        int req = 1 - bit;
        int ans1 = -1;
        if(curr->links[req]) {
            ans1 = check(curr->links[req],i-1,x,m,(ans|(1<<i)),(other|(req<<i)));
        }
        if(ans1!=-1) return ans1;
        if(curr->links[bit]) ans1 = check(curr->links[bit],i-1,x,m,ans,(other|(bit<<i)));
        else return -1;
        return ans1;
    }
};


class Solution {
public:
    vector<int> maximizeXor(vector<int>& a, vector<vector<int>>& queries) {
        trie t;
        for(auto &x: a) t.insert(x);
        vector<int> ans;
        for(auto &x: queries) {
            int a = x[0], b= x[1];
            ans.push_back(t.check(t.root,31,a,b,0,0));
        }
        return ans;
    }
};
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