<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>

struct node {
    
    node* left;
    
    node* right;

    node() : left(NULL), right(NULL) {}
};

const int N = 3000000;
node gs[N];

class Solution {
public:
    vector<int> maximizeXor(vector<int>& arr, vector<vector<int>>& queries) {

        int siz = 0;

        node* root = &gs[siz++];

        function<void(node*, int, string &)> insert;

        function<int(node*, bool, int, int, string &, string &)> query;

        vector<int> ans;

        insert = [&]( node* nodeptr, int pos, string & s) {
            if(pos>=s.length()) {
                return;
            }
            if(s[pos]=='0') {
                if(nodeptr->left==NULL) {
                    nodeptr->left = &gs[siz++];
                }
                insert( nodeptr->left, pos+1, s);
            } else {
                if(nodeptr->right==NULL) {
                    nodeptr->right = &gs[siz++];
                }
                insert( nodeptr->right, pos+1, s);
            }
        };

        query = [&]( node* nodeptr, bool is_free, int val, int pos, string & x, string & m)->int {
            if(pos>=x.length()) {
                return val;
            }
            if(is_free) {
                if(x[pos]=='0') {
                    if(nodeptr->right) {
                        return query(nodeptr->right, is_free, 2*val+1, pos+1, x, m);
                    } else {
                        return query(nodeptr->left, is_free, 2*val, pos+1, x, m);
                    }
                } else {
                    if(nodeptr->left) {
                        return query(nodeptr->left, is_free, 2*val+1, pos+1, x, m);
                    } else {
                        return query(nodeptr->right, is_free, 2*val, pos+1, x, m);
                    }
                }
            } else {
                if(m[pos]=='0') {
                    if(nodeptr->left==NULL) {
                        return -1;
                    } else {
                        return query( nodeptr->left, is_free, 2*val+(x[pos]!=m[pos]), pos+1, x, m);
                    }
                } else {
                    if(x[pos]=='0') {
                        if(nodeptr->right) {
                            if(nodeptr->left) {
                                return max(
                                    query( nodeptr->right, is_free, 2*val+1, pos+1, x, m),
                                    query( nodeptr->left, true, 2*val, pos+1, x, m)
                                );
                            } else {
                                return query( nodeptr->right, is_free, 2*val+1, pos+1, x, m); 
                            }
                        } else {
                            return query( nodeptr->left, true, 2*val, pos+1, x, m);
                        }
                    } else {
                        if(nodeptr->left) {
                            return query( nodeptr->left, true, 2*val+1, pos+1, x, m);
                        } else {
                            return query( nodeptr->right, is_free, 2*val, pos+1, x, m);
                        }
                    }
                }
            }
        };

        for( int val: arr) {
            string s = bitset<30>(val).to_string();
            insert( root, 0, s);
        }

        for( auto & _query: queries) {
            string xi = bitset<30>(_query[0]).to_string();
            string mi = bitset<30>(_query[1]).to_string();
            int val = query( root, false, 0, 0, xi, mi);
            ans.push_back(val);
        }

        for( int i=0; i<siz; i++) {
            gs[i].left = gs[i].right = NULL;
        }

        return ans;
    }
};
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