Accidentally deleted my first post. Thanks so much for your help, helped me solve this in two hours and I knew nothing of Tries before hand! Not sure why this is formatting incorrectly, but I fixed it (kinda) with p tags

// Class I use to construct the Trie:

class BinTrie:

head = {}

def add(self, integer):
    cur = self.head
    b = "{:032b}".format(integer)

    for l in b:
        l = int(l)
        if l not in cur:
            cur[l] = {}
        cur = cur[l]
    cur['*'] = True

def max_companion(self, integer):
    cur = self.head
    b = "{:032b}".format(integer)
    m_comp = ''

    for l in b:
        l = int(l)
        opp = l ^ 1
        if opp in cur:
            l = opp
        cur = cur[l]
        m_comp += str(l)
    return int(m_comp, 2)

def maxXor(arr, queries):

d = BinTrie()

out = []

for x in arr:

d.add(x)

for v in queries:

out.append(v ^ d.max_companion(v))

return out