#include #define GET_MACRO(a, b, c, NAME, ...) NAME #define rep(...) GET_MACRO(__VA_ARGS__, rep3, rep2)(__VA_ARGS__) #define rep2(i, a) rep3 (i, 0, a) #define rep3(i, a, b) for (int i = (a); i < (b); i++) #define repr(...) GET_MACRO(__VA_ARGS__, repr3, repr2)(__VA_ARGS__) #define repr2(i, a) repr3 (i, 0, a) #define repr3(i, a, b) for (int i = (b) - 1; i >= (a); i--) template inline bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); } template inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } using namespace std; typedef long long ll; struct UF { vector parent, size; UF(int n) : parent(n), size(n, 1) { rep (i, n) parent[i] = i; } int root(int x) { if (x == parent[x]) return x; else return parent[x] = root(parent[x]); } void merge(int x, int y) { x = root(x); y = root(y); if (x == y) return; if (size[x] < size[y]) swap(x, y); size[x] += size[y]; parent[y] = x; } bool same(int x, int y) { return root(x) == root(y); } }; struct Stopwatch { double start; Stopwatch() { begin(); } void begin() { start = clock(); } double elapsed() { double end = clock(); double res = (double)(end - start) / CLOCKS_PER_SEC * 1000.0; start = end; return res; } void display(string text) { cerr << text << ":" << elapsed() << "ms" << endl; } }; const int inf = 1e9; int dp0[101010], dp1[101010]; int main() { int n, m; cin >> n >> m; UF uf(n); rep (i, m) { int u, v; scanf("%d %d", &u, &v); u--; v--; uf.merge(u, v); } map mp; rep (i, n) if (uf.root(i) == i) mp[uf.size[i]]++; vector a, num; for (auto kv : mp) { a.push_back(kv.first); num.push_back(kv.second); } rep (i, 101010) dp0[i] = dp1[i] = inf; dp0[0] = 0; int sum = 0; vector> st(101010); vector ord(101010); rep (i, a.size()) { rep (j, sum + 1) { st[j].clear(); dp1[j] = inf; } sum += a[i] * num[i]; rep (j, sum + 1) { if (j - a[i] >= 0) { swap(st[j], st[j - a[i]]); ord[j] = ord[j - a[i]] + 1; } else { ord[j] = 0; } st[j].insert(dp0[j] - ord[j]); if (st[j].size() > num[i] + 1) { int pj = j - (num[i] + 1) * a[i]; auto it = st[j].find(dp0[pj] - ord[pj]); st[j].erase(it); } int cand = *st[j].begin(); chmin(dp1[j], cand + ord[j]); } swap(dp0, dp1); } rep (i, 1, n + 1) { if (dp0[i] > n) dp0[i] = 0; printf("%d\n", dp0[i] - 1); } return 0; }