<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 TrieNode:
    def __init__(self,value=-1):
        self.one = None
        self.zero = None
        self.val = value

class Solution:
    def maximizeXor(self, nums: List[int], queries: List[List[int]]) -> List[int]:
        # Trie 
        # first one that can be zero in query
        MAX_LEN = 32
        def binary(num,pad):
            ll = []
            while num>0:
                ll.append(num%2)
                num = num//2
            bin = [0 for i in range(pad)]
            # print(num,ll,pad)
            for i in range(len(ll)):
                bin[pad-i-1] = ll[i]
            return bin

        root = TrieNode()
        def construct(root,bin,num):
            for b in bin:
                if b==0:
                    if root.zero==None:
                        root.zero = TrieNode()
                    root = root.zero
                else:
                    if root.one==None:
                        root.one = TrieNode()
                    root = root.one
            root.val = num
        for num in nums:
            bina = binary(num,MAX_LEN)
            # print(bina)
            construct(root,bina,num)

        def searchTree(root,binq,binm,idx,flag):
            el = -1
            i = idx
            if root.val>-1:
                return root.val
            if flag==False:
                if binm[i]==0:
                    if root.zero==None:
                        return -1
                    else:
                        el = searchTree(root.zero,binq,binm,idx+1,False)
                else:
                    if binq[i]==1:
                        if root.zero!=None:
                            el = searchTree(root.zero,binq,binm,idx+1,True)
                        else:
                            el = searchTree(root.one,binq,binm,idx+1,False)
                    elif binq[i]==0:
                        if root.one!=None:
                            el = searchTree(root.one,binq,binm,idx+1,False)
                            if el==-1 and root.zero!=None:
                                el = searchTree(root.zero,binq,binm,idx+1,True)
                        else:
                            el = searchTree(root.zero,binq,binm,idx+1,True)
            else:
                if binq[i]==0:
                    if root.one!=None:
                        el = searchTree(root.one,binq,binm,idx+1,True)
                    else:
                        el = searchTree(root.zero,binq,binm,idx+1,True)
                elif binq[i]==1:
                    if root.zero!=None:
                        el = searchTree(root.zero,binq,binm,idx+1,True)
                    else:
                        el = searchTree(root.one,binq,binm,idx+1,True)
            return el

        
        def search(root,q,m):
            binq = binary(q,MAX_LEN)
            binm = binary(m,MAX_LEN)
            flag = False
            el = searchTree(root,binq,binm,0,flag)
            return el

        ans = []
        for q in queries:
            el = search(root,q[0],q[1])
            if el!=-1:
                el = el^q[0]
            ans.append(el)
        return ans







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