<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:
    def maximizeXor(self, nums: List[int], queries: List[List[int]]) -> List[int]:
        t = Trie()
        minNum = min(nums)
        answers = [-1] * len(queries)
        for num in nums:
            t.insert(num)
        for i in range(len(queries)):
            answers[i] = t.getMaxXORltM(queries[i][0], minNum, queries[i][1])
        return answers


class Trie:
    def __init__(self):
        self.mp = {}

    def insert(self, num):
        trav = self.mp
        for i in range(31, -1, -1):
            bit = (num >> i) & 1
            if bit not in trav:
                trav[bit] = {}
            trav = trav[bit]
        trav[-1] = {}

    def getMaxXORltM(self, query, minNum, m):
        xorSum = 0
        if minNum > m:
            return -1

        trav = self.mp
        isLessThanM = False
        # print("query", query,"mlimit", m)
        backTracki = None
        backTrackm = None
        backTrackq = None
        backTrackSum = None
        shouldBackTrack = False

        i = 31
        while i > -1:
            mbit = (m >> i) & 1  # limit
            qbit = (query >> i) & 1  # query

            if mbit == 1 and qbit == 0 and 0 in trav:# and backTracki is None:
                #print("backtrack ready")
                backTracki = i
                backTrackm = mbit
                backTrackq = qbit
                backTrackSum = xorSum
                backTrackTrav = trav
                shouldBackTrack = False

            '''print(
                i,
                "m",
                mbit,
                "q",
                qbit,
                "isLess",
                isLessThanM,
                "trav",
                list(trav.keys()),
            )'''

            if shouldBackTrack:
                # qbit = 0, trav = 0
                #print("backtracking")
                m = backTrackm
                q = backTrackq
                i = backTracki
                xorSum = backTrackSum
                trav = backTrackTrav[0]
                isLessThanM = True
                #
                backTracki = None
                backTrackm = None
                backTrackq = None
                backTrackSum = None
                backTrackTrav = None
                shouldBackTrack = False
            else:
                if isLessThanM:
                    if qbit == 1 and 0 in trav:
                        xorSum += 2**i
                        trav = trav[0]
                    elif qbit == 0 and 1 in trav:
                        xorSum += 2**i
                        trav = trav[1]
                    elif 0 in trav:
                        trav = trav[0]
                    elif 1 in trav:
                        trav = trav[1]
                else:
                    if mbit == 1:
                        if qbit == 1 and 0 in trav:
                            xorSum += 2**i
                            trav = trav[0]
                            isLessThanM = True
                        elif qbit == 0 and 1 in trav:
                            xorSum += 2**i
                            trav = trav[1]
                        elif 0 in trav:
                            trav = trav[0]
                            isLessThanM = True
                        elif 1 in trav:
                            trav = trav[1]
                    else:  # mbit==0
                        if qbit == 0 and 0 in trav:
                            trav = trav[0]
                        elif qbit == 1 and 0 in trav:
                            xorSum += 2**i
                            trav = trav[0]
                        else:
                            shouldBackTrack = True
                            i = 1 #temp val to make sure you can still cycle around
                            #print("try backtrack")

            i -= 1
        return xorSum
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