#include #include #include #include #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #ifndef __GNUC__ #include #endif using namespace std; class FastInput { bool _end; public: FastInput() : _end(false) { } operator void*() { return _end ? 0 : (void*)this; } template void read_unsigned(T *res) { T x = 0; for(char c = skip(); '0' <= c && c <= '9'; c = gc()) x = x * 10 + (c - '0'); *res = x; } template void read_signed(T *res) { char c = skip(); bool sign = false; if(c == '-') sign = true, c = gc(); T x = 0; for(; '0' <= c && c <= '9'; c = gc()) x = x * 10 + (c - '0'); *res = !sign ? x : -x; } void read_c_string(char *str, int *len) { int n = 0; for(char c = skip(); !is_delim(c); c = gc()) str[n ++] = c; str[n] = 0; *len = n; } void read_string(std::string *str) { str->clear(); for(char c = skip(); !is_delim(c); c = gc()) *str += c; } void read_line(std::string *str) { str->clear(); for(char c = gc(); c != '\n'; c = gc()) *str += c; if(!str->empty() && (*str)[str->size() - 1] == '\r') str->resize(str->size() - 1); } void read_double(double *res) { std::string buf; read_string(&buf); sscanf(buf.c_str(), "%lf", res); } void read_char(char *res) { *res = skip(); } void read_string_buf(char *res, int n) { *res = skip(); } FastInput &operator()(char &res) { read_char(&res); return *this; } FastInput &operator()(int &res) { read_signed(&res); return *this; } FastInput &operator()(unsigned &res) { read_unsigned(&res); return *this; } FastInput &operator()(long long &res) { read_signed(&res); return *this; } FastInput &operator()(unsigned long long &res) { read_unsigned(&res); return *this; } FastInput &operator()(char *res) { int len; read_c_string(res, &len); return *this; } FastInput &operator()(std::string &res) { read_string(&res); return *this; } FastInput &operator()(double &res) { read_double(&res); return *this; } template FastInput &operator()(T1 &res1, T2 &res2) { return operator()(res1)(res2); } template FastInput &operator()(T1 &res1, T2 &res2, T3 &res3) { return operator()(res1)(res2)(res3); } template FastInput &a(T *a, int n) { for(int i = 0; i < n; ++ i) operator()(a[i]); return *this; } template FastInput &operator()(vector &v) { for(size_t i = 0; i < v.size(); ++ i) operator()(v[i]); return *this; } private: static char gc() { #if defined(__GNUC__) && !defined(__MINGW32__) return (char)getchar_unlocked(); #elif defined(_MSC_VER) return (char)_getchar_nolock(); #else return (char)getchar(); #endif } static bool is_delim(char c) { return c == ' ' || c == '\t' || c == '\n' || c == '\r' || c == EOF; } char skip() { if(_end) return EOF; char c; for(c = gc(); c != -1 && is_delim(c); c = gc()) ; if(c == EOF) _end = true; return c; } } in; class FastOutput { public: template void print_unsigned(T x) { char buf[24]; int n = 0; do buf[n ++] = x % 10, x /= 10; while(x != 0); while(n > 0) pc('0' + buf[-- n]); } template void print_signed(T x) { char buf[24]; int n = 0; bool sign = false; if(x < 0) sign = true; //depends on the -x % y behaviour do buf[n ++] = x % 10, x /= 10; while(x != 0); if(!sign) { while(n > 0) pc('0' + buf[-- n]); } else { pc('-'); while(n > 0) pc('0' - buf[-- n]); } } void print_c_string(const char *str) { for(const char *p = str; *p; ++ p) pc(*p); } void print_string(const std::string &str) { print_c_string(str.c_str()); } void print_double(double x, int digits) { //|res| < 2^1024 ~ 10^308 char buf[512]; #ifdef _MSC_VER sprintf_s(buf, "%.*f", digits, x); #else sprintf(buf, "%.*f", digits, x); #endif print_c_string(buf); } void print_char(char x) { pc(x); } FastOutput &operator()(char x) { print_char(x); return *this; } FastOutput &operator()(int x) { print_signed(x); return *this; } FastOutput &operator()(unsigned x) { print_unsigned(x); return *this; } FastOutput &operator()(long long x) { print_signed(x); return *this; } FastOutput &operator()(unsigned long long x) { print_unsigned(x); return *this; } FastOutput &operator()(const char *str) { print_c_string(str); return *this; } FastOutput &operator()(const std::string &str) { print_string(str); return *this; } FastOutput &operator()(double x) { print_double(x, 10); return *this; } template FastOutput &operator()(T1 x1, T2 x2) { return operator()(x1)(x2); } template FastOutput &operator()(T1 x1, T2 x2, T3 x3) { return operator()(x1)(x2)(x3); } template FastOutput &operator()(T1 x1, T2 x2, T3 x3, T4 x4) { return operator()(x1)(x2)(x3)(x4); } private: static void pc(char c) { #if defined(__GNUC__) && !defined(__MINGW32__) putchar_unlocked(c); #elif defined(_MSC_VER) _putchar_nolock(c); #else putchar(c); #endif } } out; class FastOutputN { public: template FastOutputN &operator()(T1 x1) { out(x1)('\n'); return *this; } template FastOutputN &operator()(T1 x1, T2 x2) { out(x1, x2)('\n'); return *this; } template FastOutputN &operator()(T1 x1, T2 x2, T3 x3) { out(x1, x2, x3)('\n'); return *this; } template FastOutputN &operator()(T1 x1, T2 x2, T3 x3, T4 x4) { out(x1, x2, x3, x4)('\n'); return *this; } template FastOutputN &a(const T *a, int n) { for(int i = 0; i < n; ++ i) { if(i != 0) out(' '); out(a[i]); } out('\n'); return *this; } template FastOutputN &operator()(const vector &v) { for(size_t i = 0; i < v.size(); ++ i) { if(i != 0) out(' '); out(v[i]); } out('\n'); return *this; } } outn; struct UnionFind { vector data; void init(int n) { data.assign(n, -1); } bool unionSet(int x, int y) { x = root(x); y = root(y); if(x != y) { if(data[y] < data[x]) swap(x, y); data[x] += data[y]; data[y] = x; } return x != y; } bool findSet(int x, int y) { return root(x) == root(y); } int root(int x) { return data[x] < 0 ? x : data[x] = root(data[x]); } int size(int x) { return -data[root(x)]; } }; void update(unsigned short *dp, int n, int s, int t) { assert(s > 1); for(; n >= 0 && n % 8 != 7; -- n) { unsigned short &x = dp[n + s], y = dp[n] + t; if(y >= t && x > y) x = y; } #ifndef __GNUC__ const __m128i tttttttt = _mm_set1_epi16(t); const __m128i infs = _mm_set1_epi32(0xffffffffU); for(int i = n - 7; i >= 0; i -= 8) { const __m128i x = _mm_loadu_si128(reinterpret_cast(dp + (i + s))); const __m128i a = _mm_loadu_si128(reinterpret_cast(dp + i)); const __m128i b = _mm_add_epi16(a, tttttttt); const __m128i c = _mm_cmpeq_epi16(a, infs); const __m128i y = _mm_or_si128(b, c); const __m128i z = _mm_min_epu16(x, y); _mm_storeu_si128(reinterpret_cast<__m128i*>(dp + (i + s)), z); } #else __attribute__((aligned(16))) const unsigned char pat[16] = { 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1 }; __asm("vmovd %0, %%xmm2\n\tvpshufb %1, %%xmm2, %%xmm2":: "r"(t), "m"(pat) : "xmm2"); __asm("vpcmpeqd %%xmm3, %%xmm3, %%xmm3"::: "xmm3"); for(int i = n - 7; i >= 0; i -= 8) { const unsigned short * const p = dp + i; unsigned short * const q = dp + (i + s); __asm("vmovdqu %1, %%xmm0\n\tvpaddw %%xmm0, %%xmm2, %%xmm1\n\tvpcmpeqw %%xmm3, %%xmm0, %%xmm0\n\tvpor %%xmm0, %%xmm1, %%xmm0\n\tvpminuw %0, %%xmm0, %%xmm0\n\tvmovups %%xmm0, %0" : "=m"(*q) : "m"(*p) : "xmm0", "xmm1", "xmm2", "xmm3"); } #endif } int main() { int N; int M; while(in(N, M)) { UnionFind uf; uf.init(N); rep(i, M) { int u; int v; in(u, v), -- u, -- v; uf.unionSet(u, v); } vector counts(N + 1); rep(i, N) if(uf.root(i) == i) ++ counts[uf.size(i)]; vector > v; for(int i = 2; i <= N; ++ i) { int n = counts[i]; while(n > 0) { int m = (n + 1) / 2; v.emplace_back(i * m, m); n -= m; } } const unsigned short INFS = 0xffff; vector dp(N + 1, INFS); sort(v.begin(), v.end()); int sum = 0; dp[0] = 0; for(auto p : v) { update(&dp[0], sum, p.first, p.second); sum += p.first; } int n = counts[1]; vector > q(N + 1); int h = 0, t = 0; for(int i = 0; i <= N; ++ i) { while(h < t && q[h].first < i - n) ++ h; if(dp[i] != INFS) { int y = dp[i] - i; while(h < t && q[t - 1].second >= y) -- t; q[t ++] = {i, y}; } if(1 <= i) { if(h == t) outn("-1"); else outn(q[h].second + i - 1); } } } return 0; }