class UnionFind: def __init__(self, n): self.n = n self.parents = [-1] * n self.group = 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 False self.group -= 1 if self.parents[x] > self.parents[y]: x, y = y, x self.parents[x] += self.parents[y] self.parents[y] = x return True 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 self.group def all_group_members(self): dic = {r:[] for r in self.roots()} for i in range(self.n): dic[self.find(i)].append(i) return dic def __str__(self): return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots()) n, m = map(int, input().split()) UF = UnionFind(n) for _ in range(m): u, v = map(int, input().split()) UF.union(u - 1, v - 1) cnt = {} for r in UF.roots(): s = UF.size(r) cnt[s] = cnt.get(s, 0) + 1 dp = [1 << 60] * (n + 1) dp[0] = 0 for k, v in cnt.items(): c = 1 while v > 0: w = min(c, v) v -= c c *= 2 for i in range(n, k * w - 1, -1): dp[i] = min(dp[i], dp[i - k * w] + w) for i in range(1, n + 1): if dp[i] == 1 << 60: print(-1) else: print(dp[i] - 1)