using System; using System.IO; using System.Linq; using System.Text; using System.Collections.Generic; using System.Diagnostics; using System.Numerics; using Enu = System.Linq.Enumerable; class Program { static readonly int INF = (int)1e9; public void Solve() { int N = Reader.Int(), M = Reader.Int(); var uf = new UnionFind(N); for (int i = 0; i < M; i++) uf.Unite(Reader.Int() - 1, Reader.Int() - 1); int[] num = new int[N + 1]; foreach (var c in uf.Components()) num[c.Count]++; var dp = new int[N + 1]; for (int i = 1; i <= N; i++) dp[i] = INF; for (int size = 1; size <= N; size++) { int rem = num[size]; for (int bit = 1; rem > 0; bit <<= 1) { int add = Math.Min(rem, bit); for (int x = N; x >= size * add; x--) dp[x] = Math.Min(dp[x], dp[x - size * add] + add); rem -= add; } } Console.WriteLine(string.Join("\n", dp.Skip(1).Select(v => v == INF ? -1 : v - 1))); } class UnionFind { private int[] parent; private int[] rank; private int[] numElements; public UnionFind(int N) { parent = new int[N]; rank = new int[N]; numElements = new int[N]; for (int i = 0; i < N; i++) { parent[i] = i; numElements[i] = 1; } } public int Root(int x) { if (parent[x] == x) return x; return parent[x] = Root(parent[x]); } public bool Same(int x, int y) { return Root(x) == Root(y); } public int NumElements(int x) { return numElements[Root(x)]; } public bool Unite(int x, int y) { x = Root(x); y = Root(y); if (x == y) return false; if (rank[x] > rank[y]) { var t = x; x = y; y = t; } if (rank[x] == rank[y]) rank[y]++; parent[x] = y; numElements[y] += numElements[x]; return true; } public List[] Components() { var dic = new Dictionary>(); for (int i = 0; i < parent.Length; i++) { int root = Root(i); if (!dic.ContainsKey(root)) dic[root] = new List(); dic[root].Add(i); } return dic.Values.ToArray(); } } } class Entry { static void Main() { new Program().Solve(); } } class Reader { private static TextReader reader = Console.In; private static readonly char[] separator = { ' ' }; private static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries; private static string[] A = new string[0]; private static int i; private static void Init() { A = new string[0]; } public static void Set(TextReader r) { reader = r; Init(); } public static void Set(string file) { reader = new StreamReader(file); Init(); } public static bool HasNext() { return CheckNext(); } public static string String() { return Next(); } public static int Int() { return int.Parse(Next()); } public static long Long() { return long.Parse(Next()); } public static double Double() { return double.Parse(Next()); } public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); } public static int[] IntArray(int N) { return Enu.Range(0, N).Select(i => Int()).ToArray(); } public static int[][] IntTable(int H) { return Enu.Range(0, H).Select(i => IntLine()).ToArray(); } public static string[] StringArray(int N) { return Enu.Range(0, N).Select(i => Next()).ToArray(); } public static string Line() { return reader.ReadLine().Trim(); } private static string[] Split(string s) { return s.Split(separator, op); } private static string Next() { CheckNext(); return A[i++]; } private static bool CheckNext() { if (i < A.Length) return true; string line = reader.ReadLine(); if (line == null) return false; if (line == "") return CheckNext(); A = Split(line); i = 0; return true; } }