package problems896; import java.io.BufferedReader; import java.io.FileReader; import java.io.FileWriter; import java.io.IOException; import java.io.InputStreamReader; import java.io.PrintWriter; import java.util.ArrayList; import java.util.Arrays; import java.util.HashMap; import java.util.List; import java.util.Map; import java.util.Set; class UnionFind { private int[] parent; public UnionFind(int n) { parent = new int[n]; for (int i = 0; i < n; i++) { parent[i] = i; } } public void union(int x, int y) { x = find(x); y = find(y); if (x == y) return; parent[x] = y; } public int find(int z) { if (this.parent[z] == z) return z; parent[z] = find(parent[z]); return parent[z]; } } class Counter { private final Map map = new HashMap<>(); public Counter() { } public Counter(List ts) { this(); add(ts); } public Counter(T[] ts) { this(); add(ts); } public void add(T t) { int[] v = map.get(t); if (v == null) map.put(t, new int[]{1}); else v[0]++; } public void add(List ts) { for (T t : ts) { add(t); } } public void add(T[] ts) { for (T t : ts) { add(t); } } public int get(T t) { int[] v = map.get(t); return v == null ? 0 : v[0]; } public int set(T t, int n) { int[] v = map.get(t); if (v == null) { map.put(t, new int[]{n}); return 0; } else { int ret = v[0]; v[0] = n; return ret; } } public Set keySet() { return map.keySet(); } @Override public String toString() { StringBuilder sb = new StringBuilder("Counter{"); for (T t : map.keySet()) { sb.append(t).append(": ").append(map.get(t)[0]).append(", "); } sb.append("}"); return sb.toString(); } } public class Main { public void run() throws IOException { int N = io.nextInt(); int M = io.nextInt(); UnionFind uf = new UnionFind(N); for (int i = 0; i < M; i++) { int u = io.nextInt(); int v = io.nextInt(); uf.union(u - 1, v - 1); } Counter co = new Counter<>(); for (int i = 0; i < N; i++) { co.add(uf.find(i)); } Counter gc = new Counter<>(); for (Integer k : co.keySet()) { gc.add(co.get(k)); } int inf = N + 10; int[] dp = new int[N + 1]; Arrays.fill(dp, inf); dp[0] = -1; for (Integer g : gc.keySet()) { for (int i = N - g; i >= 0; i--) { if (dp[i] != inf) { int a = gc.get(g); for (int j = g; j <= g * a; j += g) { dp[i + j] = Math.min(dp[i + j], dp[i] + 1); } } } } for (int i = 1; i <= N; i++) { io.out.println(dp[i] != inf ? dp[i] : -1); } } // @formatter:off private static final int mod = (int) 1e9 + 7; final IOFast io = new IOFast(); void main() throws IOException { try { run(); } catch (RuntimeException e) { e.printStackTrace(); } finally { io.out.flush(); } } public static void main(String[] args) throws IOException { new Main().main(); } public static String dtos(double x, int n) { StringBuilder sb = new StringBuilder(); if (x < 0) { sb.append('-'); x = -x; } x += Math.pow(10, -n) / 2; sb.append((long) x); sb.append("."); x -= (long) x; for (int i = 0; i < n; i++) { x *= 10; sb.append((int) x); x -= (int) x; } return sb.toString(); } public static class IOFast { private BufferedReader in = new BufferedReader(new InputStreamReader(System.in)); private PrintWriter out = new PrintWriter(System.out); void setFileIn(String ins) throws IOException { in.close(); in = new BufferedReader(new FileReader(ins)); } void setFileOut(String outs) throws IOException { out.flush(); out.close(); out = new PrintWriter(new FileWriter(outs)); } void setFileIO(String ins, String outs) throws IOException { setFileIn(ins); setFileOut(outs); } private static int pos, readLen; private static final char[] buffer = new char[1024 * 8]; private static char[] str = new char[500*8*2]; private static boolean[] isDigit = new boolean[256]; private static boolean[] isSpace = new boolean[256]; private static boolean[] isLineSep = new boolean[256]; static { for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; } isDigit['-'] = true; isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true; isLineSep['\r'] = isLineSep['\n'] = true; } public int read() throws IOException { if(pos >= readLen) { pos = 0; readLen = in.read(buffer); if(readLen <= 0) { throw new RuntimeException(); } } return buffer[pos++]; } public int nextInt() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; int ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; } public long nextLong() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; long ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; } public char nextChar() throws IOException { while(true) { final int c = read(); if(!isSpace[c]) { return (char)c; } } } int reads(int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } if(str.length == len) { char[] rep = new char[str.length * 3 / 2]; System.arraycopy(str, 0, rep, 0, str.length); str = rep; } str[len++] = (char)c; } } catch(RuntimeException e) { ; } return len; } public char[] nextLine() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isLineSep); try { if(str[len-1] == '\r') { len--; read(); } } catch(RuntimeException e) { ; } return Arrays.copyOf(str, len); } public String nextString() throws IOException { return new String(next()); } public char[] next() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); return Arrays.copyOf(str, len); } public double nextDouble() throws IOException { return Double.parseDouble(nextString()); } public long[] nextLongArray(final int n) throws IOException { final long[] res = new long[n]; for(int i = 0; i < n; i++) { res[i] = nextLong(); } return res; } public int[] nextIntArray(final int n) throws IOException { final int[] res = new int[n]; for(int i = 0; i < n; i++) { res[i] = nextInt(); } return res; } public int[][] nextIntArray2D(final int n, final int k) throws IOException { final int[][] res = new int[n][]; for(int i = 0; i < n; i++) { res[i] = nextIntArray(k); } return res; } public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException { final int[][] res = new int[n][k+1]; for(int i = 0; i < n; i++) { for(int j = 0; j < k; j++) { res[i][j] = nextInt(); } res[i][k] = i; } return res; } public double[] nextDoubleArray(final int n) throws IOException { final double[] res = new double[n]; for(int i = 0; i < n; i++) { res[i] = nextDouble(); } return res; } } // @formatter:on }