Solution.py

class UnionFind:
    def __init__(self, n):
        self.p = list(range(n))
        self.size = [1] * n

    def find(self, x):
        if self.p[x] != x:
            self.p[x] = self.find(self.p[x])
        return self.p[x]

    def union(self, a, b):
        pa, pb = self.find(a), self.find(b)
        if pa == pb:
            return False
        if self.size[pa] > self.size[pb]:
            self.p[pb] = pa
            self.size[pa] += self.size[pb]
        else:
            self.p[pa] = pb
            self.size[pb] += self.size[pa]
        return True


class Solution:
    def areConnected(
        self, n: int, threshold: int, queries: List[List[int]]
    ) -> List[bool]:
        uf = UnionFind(n + 1)
        for a in range(threshold + 1, n + 1):
            for b in range(a + a, n + 1, a):
                uf.union(a, b)
        return [uf.find(a) == uf.find(b) for a, b in queries]