Buggy python submission (verdict: Time Limit Exceeded):
import sys
readline = sys.stdin.readline

class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


def main():
    N, M = map(int, readline().rstrip().split())
    inp = [tuple(map(int, readline().rstrip().split())) for _ in range(M)]
    uf = UnionFind(N)
    res = [N * (N-1) // 2]
    res_0 = res[0]

    for a, b in inp[::-1][:-1]:
        uf.union(a-1, b-1)
        v = 0
        for members in uf.all_group_members().values():
            num_member = len(members)
            v += num_member * (num_member - 1) // 2

        res.append(res_0 - v)

    print(*res[::-1], sep='\n')

if __name__ == '__main__':
    main()

Fixed submission:
import sys
readline = sys.stdin.readline

class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


def main():
    N, M = map(int, readline().rstrip().split())
    inp = [tuple(map(int, readline().rstrip().split())) for _ in range(M)]
    uf = UnionFind(N)
    res = [N * (N-1) // 2]
    res_0 = res[0]

    for a, b in inp[::-1][:-1]:
        if uf.same(a-1, b-1):
            res.append(res[-1])
        else:
            x = uf.find(a-1)
            y = uf.find(b-1)
            res.append(res[-1] - uf.size(x) * uf.size(y))
            uf.union(a-1, b-1)

    print(*res[::-1], sep='\n')

if __name__ == '__main__':
    main()